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MAX-CUT BY EXCLUDING BIPARTITE SUBGRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  08 November 2022

SHUFEI WU Open the ORCID record for SHUFEI WU [Opens in a new window]  and
AMIN LI Open the ORCID record for AMIN LI [Opens in a new window]
SHUFEI WU*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Henan 454003, PR China
AMIN LI
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Henan 454003, PR China e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

For a graph G, let $f(G)$ denote the maximum number of edges in a bipartite subgraph of G. Given a positive integer m and 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 prove bounds on $f(m,H)$ for some bipartite graphs H and give a bound for a conjecture of Alon et al. [‘MaxCut in H-free graphs’, Combin. Probab. Comput. 14 (2005), 629–647] concerning $f(m,K_{4,s})$.

Keywords

H-free graphmax-cutbipartite subgraph

MSC classification

Primary: 05C70: Factorization, matching, partitioning, covering and packing
Secondary: 05C35: Extremal problems 05C75: Structural characterization of families of graphs
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 177 - 186
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Supported by the National Natural Science Foundation of China (No. 11801149).

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