科研之友
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摘要
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 T-k on k vertices, we determine the threshold bias for the (1 : b) T-k-tournament game on K-n. We also look at the (1 : 1) T-k-tournament game played on the edge set of a random graph G(n,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.
- 出版日期2015-9-4
