Weak Positional Games on Hypergraphs of Rank Three

Weak Positional Games on Hypergraphs of Rank Three

Blog Article

Gravy and Sauce Boats 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 Time Release result is based on a new type of decomposition theorem which might lead to a better understanding of weak positional games in general.