On the chromatic index of almost all graphs

P. Erdos, Robin J. Wilson

Research output: Contribution to journalArticle

47 Citations (Scopus)


Vizing has shown that if G is a simple graph with maximum vertex-degree ρ{variant}, then the chromatic index of G is either ρ{variant} or ρ{variant} + 1. In this note we prove that almost all graphs have a unique vertex of maximum degree, and we deduce that almost all graphs have chromatic index equal to their maximum degree. This settles a conjecture of the second author (in "Proceedings of the Fifth British Combinatorial Conference 1975").

Original languageEnglish
Pages (from-to)255-257
Number of pages3
JournalJournal of Combinatorial Theory, Series B
Issue number2-3
Publication statusPublished - Jan 1 1977


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this