Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2003-07

April 2003

How Many Graphs are Unions of k-Cliques?

Béla Bollobás and Graham R. Brightwell


We study the number F[n;k] of n-vertex graphs that can be written as the edge-union of k-vertex cliques. We obtain reasonably tight estimates for F[n;k] in the cases (i) ~ k=n-o(n) and (ii) ~ k=o(n) but k/log n --> infinity. We also show that F[n;k] exhibits a phase transition around k = log2 n. We leave open several potentially interesting cases, and raise some other questions of a similar nature.

A PDF file (208 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-2003-07, 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 7732.
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 2005

Last changed: Wed 9 Feb 2005
For comments go to: http://www.maths.lse.ac.uk/webmaster.html