MaxCut in H-free graphs

Noga Mordechai Alon, Michael Krivelevich, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

For a graph G, let f(G) denote the maximum number of edges in a cut 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. In this paper we study this function for various graphs H. In particular we show that for any graph H obtained by connecting a single vertex to all vertices of a fixed nontrivial forest, there is a c(H)> 0 such that f(m,H) ≥ m/2 + c(H)m4/5, and that this is tight up to the value of $c(H)$. We also prove that for any even cycle $C_{2k}$ there is a c(k)> 0 such that f(m,C2k) ≥ m/2 + c(k) m(2k+1)/(2k+2), and that this is tight, up to the value of $c(k)$, for 2k ∈ {4,6,10\}. The proofs combine combinatorial, probabilistic and spectral techniques.

Original languageEnglish (US)
Pages (from-to)629-647
Number of pages19
JournalCombinatorics Probability and Computing
Volume14
Issue number5-6
DOIs
StatePublished - Nov 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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