Bipartite subgraphs and quasi-randomness

Authors

Jozef Skokan, University of Illinois Urbana-Champaign
Lubos Thoma, University of Rhode Island

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, e.g., Journal

Graphs and Combinatorics

Volume

20

Issue

2

Citation/Publisher Attribution

Skokan, Jozef, and Lubos Thoma. "Bipartite subgraphs and quasi-randomness." Graphs and Combinatorics 20, 2 (2004): 255-262. doi: 10.1007/s00373-004-0556-1.