Weak Positional Games on Hypergraphs of Rank Three

Weak Positional Games on Hypergraphs of Rank Three

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In a weak positional invertatop squeeze bottle game, two players, Maker and Breaker, alternately claim vertices of a hypergraph until either Maker wins by getting a complete edge or all vertices are taken without this happening, a Breaker win.For the class of almost-disjoint hypergraphs of rank three (edges with up to three vertices only and edge-intersections on at most one merlin wizard costume vertex) we show how to find optimal strategies in polynomial time.Our result is based on a new type of decomposition theorem which might lead to a better understanding of weak positional games in general.