A remark on the tournament game

Abstract

We study the Maker-Breaker tournament game played on the edge set of a given graph G. Two players, Maker and Breaker, claim unclaimed edges of G in turns, while Maker additionally assigns orientations to the edges that she claims. If by the end of the game Maker claims all the edges of a pre-defined goal tournament, she wins the game. Given a tournament Tk on k vertices, we determine the threshold bias for the (1: b) Tk-tournament game on Kn. We also look at the (1: 1) Tk- tournament game played on the edge set of a random graph Gn,p and determine the threshold probability for Maker's win. We compare these games with the clique game and discuss whether a random graph intuition is satisfied.