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.

A PDF file (243 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2006-10, together with your name and postal address to:
CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.
Phone: +44(0)-20-7955 7494.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk 


Introduction to the CDAM Research Report Series.
CDAM Homepage.


Copyright © London School of Economics & Political Science 2006