The number of cliques in graphs of given order and size

Details The number of cliques in graphs of given order and size The number of cliques in graphs of given order and size

2007-10-11

arxiv.org/abs/0710.2305v2

Mathematics

Combinatorics

This interim version is aimed to correct an error in the first version of the paper. The scope of the main result is reduced,

Scientific paper

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. In our proof, a
combinatorial strategy is coupled with extensive analytical arguments.

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