Positional Games

Positional games are a branch of combinatorics, researching a variety of twoplayer games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs. It is closely connected to many other combinatorial disciplines such as Ramsey theory, extremal graph and set theory, probabilistic combinatorics, and to computer science. We survey the basic notions of the field, its approaches and tools, as well as numerous recent advances, standing open problems and promising research directions. Mathematics Subject Classification (2010). Primary 05C57, 91A46; Secondary 05C80, 05D05, 05D10, 05D40.

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