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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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The number of cliques of given order and size
by
Vladimir Nikiforov
University of Memphis, Memphis, TN

Let k_r(n, m) denote the minimum number of r-cliques in graphs with n vertices and m edges. For r=3, 4 we give a lower bound on k_r(n, m) that approximates k_r(n, m) with an error smaller than n^r/(n^2-2m). The solution is based on a constraint minimization of certain multilinear forms.

Date received: April 23, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-34.