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About: Clique game     Goto   Sponge   NotDistinct   Permalink

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The clique game is a positional game where two players alternately pick edges, trying to occupy a complete clique of a given size. The game is parameterized by two integers n > k. The game-board is the set of all edges of a complete graph on n vertices. The winning-sets are all the cliques on k vertices. There are several variants of this game: The clique game (in its strong-positional variant) was first presented by Paul Erdős and John Selfridge, who attributed it to Simmons. They called it the Ramsey game, since it is closely related to Ramsey's theorem (see below).