Forbidden induced bipartite graphs
Forbidden induced bipartite graphs
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禁止诱导二部图
作者：
Peter Allen
鉴于固定的两分图H，我们研究了不包含H的N顶点上两分图的生长渐近速度，每当H包含循环或两分的循环速度时，增长为$ {{2}}^{\ omega（{{n}}}^{{{{6}}} \ aver {{5}}}} $。我们能够找到$ {{n}}^{{{cn}}}}+{{o}}}（{{n}}}} $的上限和下限。 c的正确值
Given a fixed bipartite graph H, we study the asymptotic speed of growth of the number of bipartite graphs on n vertices which do not contain an induced copy of H. Whenever H contains either a cycle or the bipartite complement of a cycle, the speed of growth is ${{2}}^{\Omega({{n}}^{{{{6}}\over {{5}}}})}$. For every other bipartite graph except the path on seven vertices, we are able to find both upper and lower bounds of the form ${{n}}^{{{cn}}+{{o}}({{n}})}$. In many cases we are able to determine the correct value of c. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 219–241, 2009