Title

Large joints in graphs

Abstract

We show that if r≥s≥2,n>r8, and G is a graph of order n containing as many r-cliques as the r-partite Turán graph of order n, then G has more than nr-1/r2r+12 cliques sharing a common edge unless G is isomorphic to the r-partite Turán graph of order n. This structural result generalizes a previous result that has been useful in extremal graph theory. © 2010 Elsevier Ltd.

Publication Title

European Journal of Combinatorics

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