Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2006-10

September 2006

Forbidden Induced Bipartite Graphs

Peter Allen

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 faster than n^{cn} for any c. 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.

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