The (a, b)-monochromatic transversal game on clique-hypergraphs of powers of cycles

Wilder P Mendes , Simone Dantas , Sylvain Gravier (1) , Rodrigo Marinho

1 IF - Institut Fourier

We introduce the (a, b)-monochromatic transversal game where Alice and Bob alternately colours a and b vertices of a hypergraph, respectively. Alice, who colours the vertices with red, wins the game if she obtains a red transver-sal and Bob wins it if he does not let it happen. Both players are enabled to start the game and they play optimally. We analyze the game played on clique-hypergraphs of powers of cycles and we show many strategies that, depending on the choice of the parameters, allow a specific player to win the game.

Mots clés: Combinatorial games; hypergraphs; powers of cycles; transversal

Domaines: Mathématique discrète [cs.DM]

Wilder P Mendes, Simone Dantas, Sylvain Gravier, Rodrigo Marinho. The (a, b)-monochromatic transversal game on clique-hypergraphs of powers of cycles. LAGOS 2021, 2021, Sao Paulo, Brazil. ⟨hal-03015815v2⟩