Breaking Symmetry on Complete Bipartite Graphs of Odd Size
نویسنده
چکیده
Players A and B alternatively colour edges of a graph G, red and blue respectively. Let Lsym(G) be the largest number of moves during which B can keep the red and blue subgraphs isomorphic, no matter how A plays. This function was introduced by Harary, Slany and Verbitsky who in particular showed that for complete bipartite graphs we have Lsym(Km,n) = mn 2 if mn is even and that Lsym(K2m+1,2n+1) ≥ max(m,n). Here we prove that Lsym(K2m+1,2n+1) = O(n), if m ≤ n ≤ m, answering a question posed by Harary, Slany and Verbitsky.
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تاریخ انتشار 2003