8 papers
Maker-Breaker is solved in polynomial time on hypergraphs of rank 3
Florian Galliot, Sylvain Gravier, Isabelle Sivignon
In the Maker-Breaker positional game, Maker and Breaker take turns picking vertices of a hypergraph , and Maker wins if and only if she possesses all the vertices of some edge o…
The disjoint separators problem in graphs
Thomas Delépine, Florian Galliot, Yannick Mogge +2
We study the disjoint separators problem in graphs, an analogue of the famous disjoint paths problem. Given a graph and four pairwise disjoint subsets of vertices , ,…
4-uniform Maker-Breaker and Maker-Maker games are PSPACE-complete
Florian Galliot
We study two positional games played on hypergraphs, whose edges may be interpreted as winning sets. Two players take turns picking a previously unpicked vertex of the hypergraph.…
A unified convention for achievement positional games
Florian Galliot, Jonas Sénizergues
We introduce achievement positional games, a convention for positional games which encompasses the Maker-Maker and Maker-Breaker conventions. We consider two hypergraphs, one red a…
A two-player version of the assignment problem
Florian Galliot, Nacim Oijid, Jonas Sénizergues
We introduce the competitive assignment problem, a two-player version of the well-known assignment problem. Given a set of tasks and a set of agents with different efficiencies for…
Token positional games
Guillaume Bagan, Quentin Deschamps, Florian Galliot +2
The classical Maker-Breaker positional game is played on a board which is a hypergraph , with two players, Maker and Breaker, alternately claiming vertices of $\mathca…