https://hal.inria.fr/hal-01184379Kutz, MartinMartinKutzMPII - Max-Planck-Institut für Informatik - Max-Planck-GesellschaftWeak Positional Games on Hypergraphs of Rank ThreeHAL CCSD2005hypergraphpositional gamedecomposition[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]Episciences Iam, CoordinationStefan Felsner2015-08-17 08:42:572018-09-20 07:54:022015-08-17 15:34:18enConference papershttps://hal.inria.fr/hal-01184379/document10.46298/dmtcs.3422application/pdf1In 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.