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Weak Positional Games on Hypergraphs of Rank Three

Abstract : In a weak positional 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 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.
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Martin Kutz. Weak Positional Games on Hypergraphs of Rank Three. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.31-36, ⟨10.46298/dmtcs.3422⟩. ⟨hal-01184379⟩

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