"\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u30B0\u30E9\u30D5"@ja . "En el campo matem\u00E1tico de la teor\u00EDa de grafos, el grafo de Petersen es un grafo no dirigido con 10 v\u00E9rtices y 15 aristas . Es un grafo peque\u00F1o que sirve como ejemplo y contraejemplo para muchos problemas en la teor\u00EDa de grafos. El grafo de Petersen lleva el nombre de Julius Petersen, quien en 1898 lo construy\u00F3 para ser el grafo c\u00FAbico sin puentes m\u00E1s peque\u00F1o que no se puede 3-colorear. \u200B Donald Knuth afirma que el grafo de Petersen es \"una configuraci\u00F3n notable que sirve como contraejemplo a muchas predicciones optimistas sobre qu\u00E9 podr\u00EDa ser cierto en un grafo en general.\"\u200B"@es . . "\uD398\uD14C\uB974\uC13C \uADF8\uB798\uD504"@ko . "194926"^^ . . . . . "2"^^ . . . "\u5F7C\u5F97\u68EE\u5716\u662F\u4E00\u4E2A\u753110\u4E2A\u9876\u70B9\u548C15\u6761\u8FB9\u6784\u6210\u7684\u65E0\u5411\u56FE\u3002\u5176\u6700\u4E3A\u4EBA\u719F\u77E5\u7684\u9020\u578B\u4E3A\u4E00\u4E2A\u4E94\u8FB9\u5F62\u5185\u5305\u542B\u4E00\u4E2A\u4E94\u89D2\u661F\u3002\u5F7C\u5F97\u68EE\u5716\u7531\u4E39\u9EA6\u54E5\u672C\u54C8\u6839\u5927\u5B66\u6570\u5B66\u6559\u6388Julius Peter Christian Petersen\u4E8E1898\u5E74\u63D0\u51FA\u3002\u7531\u4E8E\u5176\u6709\u8DA3\u7684\u6027\u8D28\uFF0C\u5B83\u5E38\u5E38\u7528\u4E8E\u8BC1\u660E\u4E2D\u7684\u4F8B\u5B50\u6216\u53CD\u4F8B\u3002"@zh . . . "3"^^ . . . . . . . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430"@uk . . . . "No campo da matem\u00E1tica da teoria dos grafos o grafo de Petersen \u00E9 um grafo n\u00E3o-orientado com 10 v\u00E9rtices e 15 arestas. \u00C9 um pequeno grafo que serve como um exemplo \u00FAtil e contra-exemplo para muitos problemas em teoria dos grafos. O grafo de Petersen \u00E9 nomeado em honra a Julius Petersen, que em 1898 construiu o menor grafo c\u00FAbico sem ponte cujas arestas n\u00E3o podem ser coloridas com somente tr\u00EAs cores. Embora o grafo seja geralmente creditado a Petersen, ele tinha, de facto, aparecido pela primeira vez 12 anos antes, em 1886. Donald Knuth afirma que o grafo de Petersen \u00E9 \"uma configura\u00E7\u00E3o not\u00E1vel que serve como um contra-exemplo para muitas previs\u00F5es otimistas sobre o que poderia ser verdade para os grafos em geral.\""@pt . . . . "Dalam teori graf, salah satu disiplin ilmu matematika, graf Petersen merupakan salah satu graf istimewa yang terkenal karena menjadi bukti penyangkal beberapa konjektur dalam teori graf. Graf ini dinamai atas matematikawan Denmark, Julius Petersen, ketika dia mengkonstruksi graf ini sebagai sebuah contoh graf kubik tanpa jembatan yang tidak memiliki 3-pewarnaan-sisi. Donald Knuth, dalam bukunya \"The Art of Computer Programming\" berpendapat bahwa struktur graf ini sangat istimewa. Banyak sekali sifat-sifat dalam teori graf yang sepintas terasa benar namun ternyata terbukti salah di graf ini."@in . . . . . . . "1886"^^ . . "No campo da matem\u00E1tica da teoria dos grafos o grafo de Petersen \u00E9 um grafo n\u00E3o-orientado com 10 v\u00E9rtices e 15 arestas. \u00C9 um pequeno grafo que serve como um exemplo \u00FAtil e contra-exemplo para muitos problemas em teoria dos grafos. O grafo de Petersen \u00E9 nomeado em honra a Julius Petersen, que em 1898 construiu o menor grafo c\u00FAbico sem ponte cujas arestas n\u00E3o podem ser coloridas com somente tr\u00EAs cores. Embora o grafo seja geralmente creditado a Petersen, ele tinha, de facto, aparecido pela primeira vez 12 anos antes, em 1886."@pt . . . . . . . "Petersen graph"@en . "Grafo de Petersen"@pt . "Grafo de Petersen"@es . . . . . "2"^^ . "\uD398\uD14C\uB974\uC13C \uADF8\uB798\uD504(Petersen graph)\uB294 10\uAC1C\uC758 \uAF2D\uC9D3\uC810\uACFC 15\uAC1C\uC758 \uBCC0\uC774 \uC788\uB294 \uBB34\uBC29\uD5A5 \uADF8\uB798\uD504\uC774\uB2E4. \uD398\uD14C\uB974\uC13C \uADF8\uB798\uD504\uB294 \uC728\uB9AC\uC6B0\uC2A4 \uD398\uD14C\uB974\uC13C\uC758 \uC774\uB984\uC744 \uB530\uC11C \uC9C0\uC5B4\uC84C\uB2E4."@ko . . . "Der Petersen-Graph (benannt nach dem d\u00E4nischen Mathematiker Julius Petersen) ist ein 3-regul\u00E4rer (also kubischer) Graph mit 10 Knoten. Das bedeutet, dass jeder der Knoten drei Nachbarn hat, die Gradfolge ist also (3,3,3,3,3,3,3,3,3,3). Der Petersen-Graph ist in der Graphentheorie ein oft verwendetes Beispiel und Gegenbeispiel. Er tritt auch in der tropischen Geometrie auf. Eigenschaften des Petersen-Graphen: \n* Kubisch bzw. 3-regul\u00E4r (per Definition) \n* Nicht planar \n* Zusammenh\u00E4ngend \n* Symmetrisch \n* Die L\u00E4nge des k\u00FCrzesten Kreises ist 5 \n* Enth\u00E4lt keinen Hamilton-Kreis \n* Kleinster hypohamiltonscher Graph \n* Chromatische Zahl (Graphentheorie) 3 \n* Chromatischer Index (Graphentheorie) 4 \n* Ist kein Cayley-Graph, obwohl er regul\u00E4r und lokal-endlich ist. Der Petersen-Graph geh\u00F6rt zu einer Gruppe von zusammenh\u00E4ngenden, br\u00FCckenlosen und nicht planaren Graphen, die als \u201E\u201C bezeichnet werden. Siehe auch: Typen von Graphen in der Graphentheorie in Graph (Graphentheorie)"@de . . . . . . . "Petersen graph"@en . . . . . . . "Alfred Kempe"@en . . . "10"^^ . . "En l'\u00E0mbit matem\u00E0tic de la teoria de grafs, el graf de Petersen \u00E9s un graf no dirigit amb 10 v\u00E8rtexs i 15 arestes. \u00C9s un graf petit que serveix com a exemple i com a contraexemple per a molts problemes de teoria de grafs. El graf de Petersen rep aquest nom pel matem\u00E0tic dan\u00E8s Julius Petersen, qui el va construir l'any 1898 com el m\u00E9s petit sense que no admet una 3-aresta-coloraci\u00F3. Donald Knuth afirma que el graf de Petersen \u00E9s"@ca . . . . . . . . . . . . . . . . . . . "Graf Petersena to graf o ciekawych w\u0142asno\u015Bciach cz\u0119sto u\u017Cywany w teorii graf\u00F3w. Nazwa pochodzi od nazwiska matematyka J. Petersena, kt\u00F3remu przypisuje si\u0119 pierwsz\u0105 publikacj\u0119 na temat grafu w 1898 roku. \n* Graf Petersena \n* Graf Petersena narysowany z dwoma przeci\u0119ciami. \n* Graf Petersena narysowany tak, \u017Ce wszystkie kraw\u0119dzie s\u0105 tej samej d\u0142ugo\u015Bci."@pl . "Graf Petersena"@pl . . "Grafo di Petersen"@it . . "Der Petersen-Graph (benannt nach dem d\u00E4nischen Mathematiker Julius Petersen) ist ein 3-regul\u00E4rer (also kubischer) Graph mit 10 Knoten. Das bedeutet, dass jeder der Knoten drei Nachbarn hat, die Gradfolge ist also (3,3,3,3,3,3,3,3,3,3). Der Petersen-Graph ist in der Graphentheorie ein oft verwendetes Beispiel und Gegenbeispiel. Er tritt auch in der tropischen Geometrie auf. Eigenschaften des Petersen-Graphen: Der Petersen-Graph geh\u00F6rt zu einer Gruppe von zusammenh\u00E4ngenden, br\u00FCckenlosen und nicht planaren Graphen, die als \u201E\u201C bezeichnet werden."@de . . "Nel campo matematico della teoria dei grafi, il grafo di Petersen \u00E8 un grafo non orientato con 10 vertici e 15 spigoli. \u00C8 un piccolo grafo che serve come utile esempio e controesempio per molti problemi di teoria dei grafi. Il grafo di Petersen prende il nome da Julius Petersen, che nel 1898 lo costru\u00EC per essere il pi\u00F9 piccolo grafo cubico privo di ponti senza nessuna colorazione dei tre spigoli. Donald Knuth afferma che il grafo di Petersen \u00E8 \"una notevole configurazione che serve da controesempio a molte previsioni ottimistiche su ci\u00F2 che potrebbe essere vero per i grafi in generale\"."@it . "Dalam teori graf, salah satu disiplin ilmu matematika, graf Petersen merupakan salah satu graf istimewa yang terkenal karena menjadi bukti penyangkal beberapa konjektur dalam teori graf. Graf ini dinamai atas matematikawan Denmark, Julius Petersen, ketika dia mengkonstruksi graf ini sebagai sebuah contoh graf kubik tanpa jembatan yang tidak memiliki 3-pewarnaan-sisi. Donald Knuth, dalam bukunya \"The Art of Computer Programming\" berpendapat bahwa struktur graf ini sangat istimewa. Banyak sekali sifat-sifat dalam teori graf yang sepintas terasa benar namun ternyata terbukti salah di graf ini."@in . . "\u4F69\u7279\u68EE\u5716"@zh . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u2014 \u043D\u0435\u043E\u0440\u0456\u0454\u043D\u0442\u043E\u0432\u0430\u043D\u0438\u0439 \u0433\u0440\u0430\u0444 \u0437 10 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0456 15 \u0440\u0435\u0431\u0440\u0430\u043C\u0438. \u0426\u0435 \u043D\u0435\u0432\u0435\u043B\u0438\u0447\u043A\u0438\u0439 \u0433\u0440\u0430\u0444, \u044F\u043A\u0438\u0439 \u0441\u043B\u0443\u0433\u0443\u0454 \u043A\u043E\u0440\u0438\u0441\u043D\u0438\u043C \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0430\u0431\u043E \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0434\u043B\u044F \u0431\u0430\u0433\u0430\u0442\u044C\u043E\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0430\u0444\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0438\u0439 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u042E\u043B\u0456\u0443\u0441\u0430 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430, \u044F\u043A\u0438\u0439 \u0443 1898 \u043F\u043E\u0431\u0443\u0434\u0443\u0432\u0430\u0432 \u0439\u043E\u0433\u043E \u044F\u043A \u043D\u0430\u0439\u043C\u0435\u043D\u0448\u0438\u0439 \u0431\u0435\u0437\u043C\u043E\u0441\u0442\u043E\u0432\u0438\u0439 \u043A\u0443\u0431\u0456\u0447\u043D\u0438\u0439 \u0433\u0440\u0430\u0444 \u0437 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456\u0441\u0442\u044E \u0442\u0440\u0438\u043A\u043E\u043B\u0456\u0440\u043D\u043E\u0433\u043E \u0440\u043E\u0437\u0444\u0430\u0440\u0431\u0443\u0432\u0430\u043D\u043D\u044F \u0440\u0435\u0431\u0435\u0440. \u0425\u043E\u0447\u0430 \u0433\u0440\u0430\u0444 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u0443\u044E\u0442\u044C \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0443, \u0432\u0456\u043D \u0437'\u044F\u0432\u0438\u0432\u0441\u044F \u043D\u0430 12 \u0440\u043E\u043A\u0456\u0432 \u0440\u0430\u043D\u0456\u0448\u0435, \u0432 1886. \u0414\u043E\u043D\u0430\u043B\u044C\u0434 \u041A\u043D\u0443\u0442 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u0433\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u0446\u0435 \u00AB\u0432\u0438\u0434\u0430\u0442\u043D\u0430 \u0444\u043E\u0440\u043C\u0430, \u0449\u043E \u0441\u043B\u0443\u0433\u0443\u0454 \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0434\u043B\u044F \u0431\u0430\u0433\u0430\u0442\u044C\u043E\u0445 \u043E\u043F\u0442\u0438\u043C\u0456\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0440\u043E\u0446\u0442\u0432 \u043F\u0440\u043E \u0442\u0435, \u0449\u043E \u043C\u043E\u0436\u0435 \u0431\u0443\u0442\u0438 \u043F\u0440\u0430\u0432\u0438\u043B\u044C\u043D\u0438\u043C \u0434\u043B\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u0437\u0430\u0433\u0430\u043B\u043E\u043C.\u00BB"@uk . . "Nel campo matematico della teoria dei grafi, il grafo di Petersen \u00E8 un grafo non orientato con 10 vertici e 15 spigoli. \u00C8 un piccolo grafo che serve come utile esempio e controesempio per molti problemi di teoria dei grafi. Il grafo di Petersen prende il nome da Julius Petersen, che nel 1898 lo costru\u00EC per essere il pi\u00F9 piccolo grafo cubico privo di ponti senza nessuna colorazione dei tre spigoli. Sebbene il grafo sia generalmente attribuito a Petersen, esso era apparso in realt\u00E0 12 anni prima, in un saggio di . Kempe osserv\u00F2 che i suoi vertici possono rappresentare le dieci linee della , e che i suoi spigoli rappresentano coppie di linee che non s'incontrano in un uno dei dieci punti della configurazione. Donald Knuth afferma che il grafo di Petersen \u00E8 \"una notevole configurazione che serve da controesempio a molte previsioni ottimistiche su ci\u00F2 che potrebbe essere vero per i grafi in generale\"."@it . . "Petersen\u016Fv graf je 3-regul\u00E1rn\u00ED (kubick\u00FD) graf s 10 vrcholy s \u0159adou zaj\u00EDmav\u00FDch vlastnost\u00ED. Pojmenovan\u00FD je po d\u00E1nsk\u00E9m matematikovi , kter\u00FD ho roku 1898 zkonstruoval coby nejmen\u0161\u00ED bezmost\u00FD 3-regul\u00E1rn\u00ED graf, jeho\u017E hrany nelze t\u0159emi barvami."@cs . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u2014 \u043D\u0435\u043E\u0440\u0456\u0454\u043D\u0442\u043E\u0432\u0430\u043D\u0438\u0439 \u0433\u0440\u0430\u0444 \u0437 10 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0456 15 \u0440\u0435\u0431\u0440\u0430\u043C\u0438. \u0426\u0435 \u043D\u0435\u0432\u0435\u043B\u0438\u0447\u043A\u0438\u0439 \u0433\u0440\u0430\u0444, \u044F\u043A\u0438\u0439 \u0441\u043B\u0443\u0433\u0443\u0454 \u043A\u043E\u0440\u0438\u0441\u043D\u0438\u043C \u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0430\u0431\u043E \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0434\u043B\u044F \u0431\u0430\u0433\u0430\u0442\u044C\u043E\u0445 \u043F\u0440\u043E\u0431\u043B\u0435\u043C \u0432 \u0442\u0435\u043E\u0440\u0456\u0457 \u0433\u0440\u0430\u0444\u0456\u0432. \u041D\u0430\u0437\u0432\u0430\u043D\u0438\u0439 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u042E\u043B\u0456\u0443\u0441\u0430 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430, \u044F\u043A\u0438\u0439 \u0443 1898 \u043F\u043E\u0431\u0443\u0434\u0443\u0432\u0430\u0432 \u0439\u043E\u0433\u043E \u044F\u043A \u043D\u0430\u0439\u043C\u0435\u043D\u0448\u0438\u0439 \u0431\u0435\u0437\u043C\u043E\u0441\u0442\u043E\u0432\u0438\u0439 \u043A\u0443\u0431\u0456\u0447\u043D\u0438\u0439 \u0433\u0440\u0430\u0444 \u0437 \u043D\u0435\u043C\u043E\u0436\u043B\u0438\u0432\u0456\u0441\u0442\u044E \u0442\u0440\u0438\u043A\u043E\u043B\u0456\u0440\u043D\u043E\u0433\u043E \u0440\u043E\u0437\u0444\u0430\u0440\u0431\u0443\u0432\u0430\u043D\u043D\u044F \u0440\u0435\u0431\u0435\u0440. \u0425\u043E\u0447\u0430 \u0433\u0440\u0430\u0444 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u043E \u043F\u0440\u0438\u043F\u0438\u0441\u0443\u044E\u0442\u044C \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0443, \u0432\u0456\u043D \u0437'\u044F\u0432\u0438\u0432\u0441\u044F \u043D\u0430 12 \u0440\u043E\u043A\u0456\u0432 \u0440\u0430\u043D\u0456\u0448\u0435, \u0432 1886. \u0414\u043E\u043D\u0430\u043B\u044C\u0434 \u041A\u043D\u0443\u0442 \u0441\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u0454, \u0449\u043E \u0433\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u0446\u0435 \u00AB\u0432\u0438\u0434\u0430\u0442\u043D\u0430 \u0444\u043E\u0440\u043C\u0430, \u0449\u043E \u0441\u043B\u0443\u0433\u0443\u0454 \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043A\u043B\u0430\u0434\u043E\u043C \u0434\u043B\u044F \u0431\u0430\u0433\u0430\u0442\u044C\u043E\u0445 \u043E\u043F\u0442\u0438\u043C\u0456\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0440\u043E\u0446\u0442\u0432 \u043F\u0440\u043E \u0442\u0435, \u0449\u043E \u043C\u043E\u0436\u0435 \u0431\u0443\u0442\u0438 \u043F\u0440\u0430\u0432\u0438\u043B\u044C\u043D\u0438\u043C \u0434\u043B\u044F \u0433\u0440\u0430\u0444\u0456\u0432 \u0437\u0430\u0433\u0430\u043B\u043E\u043C.\u00BB"@uk . . "PetersenGraph"@en . . . . "Graf Petersen"@in . "In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Donald Knuth states that the Petersen graph is \"a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general.\""@en . . . . . "A. B."@en . . "En el campo matem\u00E1tico de la teor\u00EDa de grafos, el grafo de Petersen es un grafo no dirigido con 10 v\u00E9rtices y 15 aristas . Es un grafo peque\u00F1o que sirve como ejemplo y contraejemplo para muchos problemas en la teor\u00EDa de grafos. El grafo de Petersen lleva el nombre de Julius Petersen, quien en 1898 lo construy\u00F3 para ser el grafo c\u00FAbico sin puentes m\u00E1s peque\u00F1o que no se puede 3-colorear. \u200B Aunque com\u00FAnmente se le da cr\u00E9dito a Petersen, en realidad apareci\u00F3 por primera vez 12 a\u00F1os antes, en un art\u00EDculo de A. B. Kempe. Kempe observ\u00F3 que sus v\u00E9rtices pueden representar las diez l\u00EDneas de la configuraci\u00F3n de Desargues, y sus bordes representan pares de l\u00EDneas que no se encuentran en uno de los diez puntos de la configuraci\u00F3n. Donald Knuth afirma que el grafo de Petersen es \"una configuraci\u00F3n notable que sirve como contraejemplo a muchas predicciones optimistas sobre qu\u00E9 podr\u00EDa ser cierto en un grafo en general.\"\u200B"@es . "The Petersen graph is most commonly drawn as a pentagon with a pentagram inside, with five spokes."@en . . "15"^^ . . . . "Petersen\u016Fv graf je 3-regul\u00E1rn\u00ED (kubick\u00FD) graf s 10 vrcholy s \u0159adou zaj\u00EDmav\u00FDch vlastnost\u00ED. Pojmenovan\u00FD je po d\u00E1nsk\u00E9m matematikovi , kter\u00FD ho roku 1898 zkonstruoval coby nejmen\u0161\u00ED bezmost\u00FD 3-regul\u00E1rn\u00ED graf, jeho\u017E hrany nelze t\u0159emi barvami."@cs . . "\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u30B0\u30E9\u30D5\uFF08\u82F1: Petersen graph\uFF09\u307E\u305F\u306F\u30DA\u30C6\u30EB\u30BB\u30F3\u30B0\u30E9\u30D5\u3068\u306F\u300110\u500B\u306E\u9802\u70B9\u306815\u500B\u306E\u8FBA\u304B\u3089\u306A\u308B\u7121\u5411\u30B0\u30E9\u30D5\u3067\u3042\u308B\u3002\u30B0\u30E9\u30D5\u7406\u8AD6\u306E\u69D8\u3005\u306A\u554F\u984C\u306E\u4F8B\u3001\u3042\u308B\u3044\u306F\u53CD\u4F8B\u3068\u3057\u3066\u3088\u304F\u4F7F\u308F\u308C\u308B\u30021898\u5E74\u3001\u30B8\u30E5\u30EA\u30A6\u30B9\u30FB\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u304C3\u8272\u8FBA\u5F69\u8272\u3067\u304D\u306A\u3044\u6700\u5C0F\u306E\u30D6\u30EA\u30C3\u30B8\u306E\u306A\u30443-\u6B63\u5247\u30B0\u30E9\u30D5\u3068\u3057\u3066\u8003\u6848\u3057\u305F\u3002\u305D\u306E\u305F\u3081\u3001\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u30B0\u30E9\u30D5\u3068\u547C\u3070\u308C\u3066\u3044\u308B\u304C\u3001\u5B9F\u969B\u306B\u306F1886\u5E74\u306B\u65E2\u306B\u8003\u6848\u3055\u308C\u3066\u3044\u305F\u3002"@ja . . . . . . "5"^^ . . . "\u5F7C\u5F97\u68EE\u5716\u662F\u4E00\u4E2A\u753110\u4E2A\u9876\u70B9\u548C15\u6761\u8FB9\u6784\u6210\u7684\u65E0\u5411\u56FE\u3002\u5176\u6700\u4E3A\u4EBA\u719F\u77E5\u7684\u9020\u578B\u4E3A\u4E00\u4E2A\u4E94\u8FB9\u5F62\u5185\u5305\u542B\u4E00\u4E2A\u4E94\u89D2\u661F\u3002\u5F7C\u5F97\u68EE\u5716\u7531\u4E39\u9EA6\u54E5\u672C\u54C8\u6839\u5927\u5B66\u6570\u5B66\u6559\u6388Julius Peter Christian Petersen\u4E8E1898\u5E74\u63D0\u51FA\u3002\u7531\u4E8E\u5176\u6709\u8DA3\u7684\u6027\u8D28\uFF0C\u5B83\u5E38\u5E38\u7528\u4E8E\u8BC1\u660E\u4E2D\u7684\u4F8B\u5B50\u6216\u53CD\u4F8B\u3002"@zh . . "1"^^ . . . . . . . . . . . . . . . "Graf de Petersen"@ca . . . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u2014 \u043D\u0435\u043E\u0440\u0438\u0435\u043D\u0442\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u044B\u0439 \u0433\u0440\u0430\u0444 \u0441 10 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0438 15 \u0440\u0451\u0431\u0440\u0430\u043C\u0438; \u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0439 \u0433\u0440\u0430\u0444, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u044B\u0439 \u0432 \u043A\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043F\u0440\u0438\u043C\u0435\u0440\u0430 \u0438 \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043C\u0435\u0440\u0430 \u0434\u043B\u044F \u043C\u043D\u043E\u0433\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0433\u0440\u0430\u0444\u043E\u0432. \u041D\u0430\u0437\u0432\u0430\u043D \u0432 \u0447\u0435\u0441\u0442\u044C \u042E\u043B\u0438\u0443\u0441\u0430 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430, \u043F\u043E\u0441\u0442\u0440\u043E\u0438\u0432\u0448\u0435\u0433\u043E \u0435\u0433\u043E \u0432 1898 \u0433\u043E\u0434\u0443 \u043A\u0430\u043A \u043D\u0430\u0438\u043C\u0435\u043D\u044C\u0448\u0438\u0439 \u043A\u0443\u0431\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0433\u0440\u0430\u0444 \u0431\u0435\u0437 \u043C\u043E\u0441\u0442\u043E\u0432, \u043D\u0435 \u0438\u043C\u0435\u044E\u0449\u0438\u0439 \u0440\u0451\u0431\u0435\u0440\u043D\u043E\u0439 \u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0438 \u0432 \u0442\u0440\u0438 \u0446\u0432\u0435\u0442\u0430. \u041F\u0440\u0438 \u044D\u0442\u043E\u043C \u043F\u0435\u0440\u0432\u043E\u0435 \u0443\u043F\u043E\u043C\u0438\u043D\u0430\u043D\u0438\u0435 \u0442\u0430\u043A\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0430 \u043E\u0442\u043C\u0435\u0447\u0435\u043D\u043E \u0432 \u0441\u0442\u0430\u0442\u044C\u0435 \u041A\u0435\u043C\u043F\u0435 1886 \u0433\u043E\u0434\u0430, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043E\u0442\u043C\u0435\u0447\u0435\u043D\u043E, \u0447\u0442\u043E \u0435\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D\u044B \u043C\u043E\u0436\u043D\u043E \u0440\u0430\u0441\u0441\u043C\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044C \u043A\u0430\u043A \u0434\u0435\u0441\u044F\u0442\u044C \u043F\u0440\u044F\u043C\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0414\u0435\u0437\u0430\u0440\u0433\u0430, \u0430 \u0440\u0451\u0431\u0440\u0430 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0442 \u043F\u0430\u0440\u044B \u043F\u0440\u044F\u043C\u044B\u0445, \u043F\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043D\u0438\u0435 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043D\u0435 \u043F\u0440\u0438\u043D\u0430\u0434\u043B\u0435\u0436\u0438\u0442 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438. \u0414\u043E\u043D\u0430\u043B\u044C\u0434 \u041A\u043D\u0443\u0442 \u043E\u0442\u043C\u0435\u0447\u0430\u0435\u0442 \u0433\u0440\u0430\u0444 \u043A\u0430\u043A \u043F\u0440\u0438\u043C\u0435\u0447\u0430\u0442\u0435\u043B\u044C\u043D\u044B\u0439 \u0442\u0435\u043C, \u0447\u0442\u043E \u0434\u0430\u0451\u0442 \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043C\u0435\u0440\u044B \u043A\u043E \u043C\u043D\u043E\u0433\u0438\u043C \u00AB\u043E\u043F\u0442\u0438\u043C\u0438\u0441\u0442\u0438\u0447\u043D\u044B\u043C\u00BB \u0432\u044B\u0441\u043A\u0430\u0437\u044B\u0432\u0430\u043D\u0438\u044F\u043C \u043E \u0433\u0440\u0430\u0444\u0430\u0445 \u0432 \u0446\u0435\u043B\u043E\u043C. \u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u043F\u043E\u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0442\u0430\u043A\u0436\u0435 \u0432 \u0442\u0440\u043E\u043F\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438: \u043A\u043E\u043D\u0443\u0441 \u043D\u0430\u0434 \u0433\u0440\u0430\u0444\u043E\u043C \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u043C \u043E\u0431\u0440\u0430\u0437\u043E\u043C \u0438\u0434\u0435\u043D\u0442\u0438\u0444\u0438\u0446\u0438\u0440\u0443\u0435\u0442\u0441\u044F \u043C\u043E\u0434\u0443\u043B\u044C\u043D\u044B\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E\u043C \u043F\u044F\u0442\u0438\u0442\u043E\u0447\u0435\u0447\u043D\u044B\u0445 \u0440\u0430\u0446\u0438\u043E\u043D\u0430\u043B\u044C\u043D\u044B\u0445 \u0442\u0440\u043E\u043F\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u043A\u0440\u0438\u0432\u044B\u0445."@ru . . . . . . . . . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430"@ru . "23256"^^ . . . . . . . . . . . "Le graphe de Petersen est, en th\u00E9orie des graphes, un graphe particulier poss\u00E9dant 10 sommets et 15 ar\u00EAtes. Il s'agit d'un petit graphe qui sert d'exemple et de contre-exemple pour plusieurs probl\u00E8mes de la th\u00E9orie des graphes. Il porte le nom du math\u00E9maticien Julius Petersen, qui l'introduisit en 1898 en tant que plus petit graphe cubique sans isthme dont les ar\u00EAtes ne peuvent \u00EAtre color\u00E9es avec trois couleurs. Il a cependant \u00E9t\u00E9 mentionn\u00E9 par Alfred Kempe pour la premi\u00E8re fois 12 ans auparavant, en 1886. Donald Knuth explique dans The Art of Computer Programming que le graphe de Petersen est \u00AB une configuration remarquable qui sert de contre-exemple \u00E0 de nombreuses pr\u00E9dictions optimistes sur ce qui devrait \u00EAtre vrai pour tous les graphes \u00BB."@fr . . . . "\uD398\uD14C\uB974\uC13C \uADF8\uB798\uD504(Petersen graph)\uB294 10\uAC1C\uC758 \uAF2D\uC9D3\uC810\uACFC 15\uAC1C\uC758 \uBCC0\uC774 \uC788\uB294 \uBB34\uBC29\uD5A5 \uADF8\uB798\uD504\uC774\uB2E4. \uD398\uD14C\uB974\uC13C \uADF8\uB798\uD504\uB294 \uC728\uB9AC\uC6B0\uC2A4 \uD398\uD14C\uB974\uC13C\uC758 \uC774\uB984\uC744 \uB530\uC11C \uC9C0\uC5B4\uC84C\uB2E4."@ko . "Petersen\u016Fv graf"@cs . . "Petersen-Graph"@de . . . "3"^^ . "En l'\u00E0mbit matem\u00E0tic de la teoria de grafs, el graf de Petersen \u00E9s un graf no dirigit amb 10 v\u00E8rtexs i 15 arestes. \u00C9s un graf petit que serveix com a exemple i com a contraexemple per a molts problemes de teoria de grafs. El graf de Petersen rep aquest nom pel matem\u00E0tic dan\u00E8s Julius Petersen, qui el va construir l'any 1898 com el m\u00E9s petit sense que no admet una 3-aresta-coloraci\u00F3. Tot i que s'acostuma a atribuir el descobriment del graf a Petersen, de fet va sorgir 12 anys abans en una publicaci\u00F3 d'Alfred Kempe. Kempe observ\u00E0 que els seus v\u00E8rtexs poden representar les 10 rectes de la , i les seves arestes representen parells de rectes que no s'intersecten a un dels 10 punts de la configuraci\u00F3. Donald Knuth afirma que el graf de Petersen \u00E9s"@ca . . . . . "4"^^ . . . . "120"^^ . "cs2"@en . . . "Petersen Graph"@en . "Graphe de Petersen"@fr . . . "\u0413\u0440\u0430\u0444 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430 \u2014 \u043D\u0435\u043E\u0440\u0438\u0435\u043D\u0442\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u044B\u0439 \u0433\u0440\u0430\u0444 \u0441 10 \u0432\u0435\u0440\u0448\u0438\u043D\u0430\u043C\u0438 \u0438 15 \u0440\u0451\u0431\u0440\u0430\u043C\u0438; \u0434\u043E\u0441\u0442\u0430\u0442\u043E\u0447\u043D\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0439 \u0433\u0440\u0430\u0444, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u0443\u0435\u043C\u044B\u0439 \u0432 \u043A\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043F\u0440\u0438\u043C\u0435\u0440\u0430 \u0438 \u043A\u043E\u043D\u0442\u0440\u043F\u0440\u0438\u043C\u0435\u0440\u0430 \u0434\u043B\u044F \u043C\u043D\u043E\u0433\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0432 \u0442\u0435\u043E\u0440\u0438\u0438 \u0433\u0440\u0430\u0444\u043E\u0432. \u041D\u0430\u0437\u0432\u0430\u043D \u0432 \u0447\u0435\u0441\u0442\u044C \u042E\u043B\u0438\u0443\u0441\u0430 \u041F\u0435\u0442\u0435\u0440\u0441\u0435\u043D\u0430, \u043F\u043E\u0441\u0442\u0440\u043E\u0438\u0432\u0448\u0435\u0433\u043E \u0435\u0433\u043E \u0432 1898 \u0433\u043E\u0434\u0443 \u043A\u0430\u043A \u043D\u0430\u0438\u043C\u0435\u043D\u044C\u0448\u0438\u0439 \u043A\u0443\u0431\u0438\u0447\u0435\u0441\u043A\u0438\u0439 \u0433\u0440\u0430\u0444 \u0431\u0435\u0437 \u043C\u043E\u0441\u0442\u043E\u0432, \u043D\u0435 \u0438\u043C\u0435\u044E\u0449\u0438\u0439 \u0440\u0451\u0431\u0435\u0440\u043D\u043E\u0439 \u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0438 \u0432 \u0442\u0440\u0438 \u0446\u0432\u0435\u0442\u0430. \u041F\u0440\u0438 \u044D\u0442\u043E\u043C \u043F\u0435\u0440\u0432\u043E\u0435 \u0443\u043F\u043E\u043C\u0438\u043D\u0430\u043D\u0438\u0435 \u0442\u0430\u043A\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0430 \u043E\u0442\u043C\u0435\u0447\u0435\u043D\u043E \u0432 \u0441\u0442\u0430\u0442\u044C\u0435 \u041A\u0435\u043C\u043F\u0435 1886 \u0433\u043E\u0434\u0430, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u043E\u0442\u043C\u0435\u0447\u0435\u043D\u043E, \u0447\u0442\u043E \u0435\u0433\u043E \u0432\u0435\u0440\u0448\u0438\u043D\u044B \u043C\u043E\u0436\u043D\u043E \u0440\u0430\u0441\u0441\u043C\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044C \u043A\u0430\u043A \u0434\u0435\u0441\u044F\u0442\u044C \u043F\u0440\u044F\u043C\u044B\u0445 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438 \u0414\u0435\u0437\u0430\u0440\u0433\u0430, \u0430 \u0440\u0451\u0431\u0440\u0430 \u043F\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043B\u044F\u044E\u0442 \u043F\u0430\u0440\u044B \u043F\u0440\u044F\u043C\u044B\u0445, \u043F\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043D\u0438\u0435 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043D\u0435 \u043F\u0440\u0438\u043D\u0430\u0434\u043B\u0435\u0436\u0438\u0442 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438."@ru . . . . "Graf Petersena to graf o ciekawych w\u0142asno\u015Bciach cz\u0119sto u\u017Cywany w teorii graf\u00F3w. Nazwa pochodzi od nazwiska matematyka J. Petersena, kt\u00F3remu przypisuje si\u0119 pierwsz\u0105 publikacj\u0119 na temat grafu w 1898 roku. \n* Graf Petersena \n* Graf Petersena narysowany z dwoma przeci\u0119ciami. \n* Graf Petersena narysowany tak, \u017Ce wszystkie kraw\u0119dzie s\u0105 tej samej d\u0142ugo\u015Bci."@pl . . . . "200"^^ . . "Kempe"@en . "Le graphe de Petersen est, en th\u00E9orie des graphes, un graphe particulier poss\u00E9dant 10 sommets et 15 ar\u00EAtes. Il s'agit d'un petit graphe qui sert d'exemple et de contre-exemple pour plusieurs probl\u00E8mes de la th\u00E9orie des graphes. Il porte le nom du math\u00E9maticien Julius Petersen, qui l'introduisit en 1898 en tant que plus petit graphe cubique sans isthme dont les ar\u00EAtes ne peuvent \u00EAtre color\u00E9es avec trois couleurs. Il a cependant \u00E9t\u00E9 mentionn\u00E9 par Alfred Kempe pour la premi\u00E8re fois 12 ans auparavant, en 1886."@fr . . . . . . . . . . . "1113352420"^^ . . "\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u30B0\u30E9\u30D5\uFF08\u82F1: Petersen graph\uFF09\u307E\u305F\u306F\u30DA\u30C6\u30EB\u30BB\u30F3\u30B0\u30E9\u30D5\u3068\u306F\u300110\u500B\u306E\u9802\u70B9\u306815\u500B\u306E\u8FBA\u304B\u3089\u306A\u308B\u7121\u5411\u30B0\u30E9\u30D5\u3067\u3042\u308B\u3002\u30B0\u30E9\u30D5\u7406\u8AD6\u306E\u69D8\u3005\u306A\u554F\u984C\u306E\u4F8B\u3001\u3042\u308B\u3044\u306F\u53CD\u4F8B\u3068\u3057\u3066\u3088\u304F\u4F7F\u308F\u308C\u308B\u30021898\u5E74\u3001\u30B8\u30E5\u30EA\u30A6\u30B9\u30FB\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u304C3\u8272\u8FBA\u5F69\u8272\u3067\u304D\u306A\u3044\u6700\u5C0F\u306E\u30D6\u30EA\u30C3\u30B8\u306E\u306A\u30443-\u6B63\u5247\u30B0\u30E9\u30D5\u3068\u3057\u3066\u8003\u6848\u3057\u305F\u3002\u305D\u306E\u305F\u3081\u3001\u30D4\u30FC\u30BF\u30FC\u30BB\u30F3\u30B0\u30E9\u30D5\u3068\u547C\u3070\u308C\u3066\u3044\u308B\u304C\u3001\u5B9F\u969B\u306B\u306F1886\u5E74\u306B\u65E2\u306B\u8003\u6848\u3055\u308C\u3066\u3044\u305F\u3002"@ja . "In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by A. B. Kempe. Kempe observed that its vertices can represent the ten lines of the Desargues configuration, and its edges represent pairs of lines that do not meet at one of the ten points of the configuration. Donald Knuth states that the Petersen graph is \"a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general.\" The Petersen graph also makes an appearance in tropical geometry. The cone over the Petersen graph is naturally identified with the moduli space of five-pointed rational tropical curves."@en . . .