Bipartite density of triangle-free subcubic graphs

Authors:
Xuding Zhu
Affiliations:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan and National Center for Theoretical Sciences, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 3
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Abstract

A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is defined as b(G)=max{|E(B)|/|E(G)|:B is a bipartite subgraph of G}. It was conjectured by Bondy and Locke that if G is a triangle-free subcubic graph, then b(G)=45 and equality holds only if G is in a list of seven small graphs. The conjecture has been confirmed recently by Xu and Yu. This note gives a shorter proof of this result.