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

Abstract

We study the (a, b)-monochromatic transversal game that is a combinatorial Maker–Breaker game where Alice and Bob alternately colour a vertices in red and b vertices in blue of a hypergraph, respectively. Either player is enabled to start the game. Alice tries to construct a hyperedge transversal, and Bob tries to prevent this. The winner is Alice if she obtains a red hyperedge transversal; otherwise, Bob wins the game if he obtains a monochromatic blue hyperedge. Maker–Breaker games were determined to be PSPACE-complete. In this work, we analyze the game played on clique-hypergraphs of powers of cycles, and we show strategies that, depending on the choice of the parameters, allow a specific player to win the game.