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MAX-CUT BY EXCLUDING BIPARTITE SUBGRAPHS
Part of:
Graph theory
Published online by Cambridge University Press: 08 November 2022
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 
$f(m,K_{4,s})$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 177 - 186
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Supported by the National Natural Science Foundation of China (No. 11801149).
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