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BIPARTITE SUBGRAPHS OF $H$-FREE GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  07 February 2017

QINGHOU ZENG  and
JIANFENG HOU
QINGHOU ZENG*
Affiliation:
Center for Discrete Mathematics, Fuzhou University, Fujian, 350003, China email qinghouzeng@hotmail.com
JIANFENG HOU
Affiliation:
Center for Discrete Mathematics, Fuzhou University, Fujian, 350003, China email jfhou@fzu.edu.cn
*
✉qinghouzeng@hotmail.com
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Abstract

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For a graph $G$, let $f(G)$ denote the maximum number of edges in a bipartite subgraph of $G$. For an integer $m$ and for a fixed graph $H$, let $f(m,H)$ denote the minimum possible cardinality of $f(G)$ as $G$ ranges over all graphs on $m$ edges that contain no copy of $H$. We give a general lower bound for $f(m,H)$ which extends a result of Erdős and Lovász and we study this function for any bipartite graph $H$ with maximum degree at most $t\geq 2$ on one side.

Keywords

H-free graphpartitionbipartite subgraph

MSC classification

Primary: 05C35: Extremal problems
Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 1 - 13
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is supported by NSFC (Grant No. 11671087) and New Century Programming of Fujian Province (Grant No. JA14028).

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