Hadwiger's conjecture for quasi-line graphs

Maria Chudnovsky, Alexandra Ovetsky Fradkin

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

A graph G is a quasi-line graph if for every vertex v ∈ V(G), the set of neighbors of v in G can be expressed as the union of two cliques. The class of quasi-line graphs is a proper superset of the class of line graphs. Hadwiger's conjecture states that if a graph G is not t-colorable then it contains Kt+1 as a minor. This conjecture has been proved for line graphs by Reed and Seymour. We extend their result to all quasi-line graphs.

Original languageEnglish (US)
Pages (from-to)17-33
Number of pages17
JournalJournal of Graph Theory
Volume59
Issue number1
DOIs
StatePublished - Sep 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Claw-free graphs
  • Hadwiger's conjecture
  • Minors

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