Almost all C 4 - free graphs have fewer than ( 1 − ε ) ex ( n , C 4 ) edges

Abstract

A graph is called H-free if it contains no copy of H. Let ex(n,H) denote the Turán number for H, i.e., the maximum number of edges that an n-vertex H-free graph may have. An old result of Kleitman and Winston states that there are 2O(ex(n,C4)) C4-free graphs on n vertices. Füredi showed that almost all C4-free graphs of order n have at least c ex(n,C4… (More)

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