On the separation conjecture in Avoider-Enforcer games

摘要

Given a fixed graph H with at least two edges and positive integers n and b, the strict (1: b) Avoider-Enforcer H-game, played on the edge set of K-n, has the following rules: In each turn Avoider picks exactly one edge, and then Enforcer picks exactly b edges. Avoider wins if and only if the subgraph containing her/his edges is H-free after all edges of K-n, are taken.