Title

Bipartite subgraphs and quasi-randomness

Document Type

Article

Date of Original Version

12-1-2004

Abstract

We say that a family of graphs script G sign = {Gn : n ≥ 1} is p-quasi-random, 0 < p < 1, if it shares typical properties of the random graph G(n, p); for a definition, see below. We denote by script Q signw(p) the class of all graphs H for which e(Gn) ≥ (1 + o(1))p(2n) and the number of not necessarily induced labeled copies of H in Gn is at most (1 + o(1))pe(H)n v(H) imply that script G sign is p-quasi-random. In this note, we show that all complete bipartite graphs Ka,b, a, b ≥ 2, belong to script Q signw(p) for all 0 < p < 1. © Springer-Verlag 2004.

Publication Title

Graphs and Combinatorics

Volume

20

Issue

2

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