On the chromatic index of almost all graphs

P. Erdős, Robin J. Wilson

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

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
Volume23
Issue number2-3
DOIs
Publication statusPublished - 1977

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Chromatic Index
Maximum Degree
Vertex Degree
Graph in graph theory
Simple Graph
Deduce
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On the chromatic index of almost all graphs. / Erdős, P.; Wilson, Robin J.

In: Journal of Combinatorial Theory. Series B, Vol. 23, No. 2-3, 1977, p. 255-257.

Research output: Contribution to journalArticle

Erdős, P. ; Wilson, Robin J. / On the chromatic index of almost all graphs. In: Journal of Combinatorial Theory. Series B. 1977 ; Vol. 23, No. 2-3. pp. 255-257.
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