Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2003-07 April 2003

Abstract

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.

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