Edge coloring multigraphs without small dense subsets

P. E. Haxell, Henry Kierstead

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose G is a multigraph with maximum degree Δ, such that no vertex subset S of odd size at most Δ induces more than (Δ+1)(|S|-1)/2 edges. Then G has an edge coloring with Δ+1 colors. Here we prove a weakened version of this statement.

Original languageEnglish (US)
Pages (from-to)2502-2506
Number of pages5
JournalDiscrete Mathematics
Volume338
Issue number12
DOIs
StatePublished - Jul 13 2015

Fingerprint

Multigraph
Edge Coloring
Coloring
Color
Chromatic Index
Subset
Maximum Degree
Odd
Vertex of a graph

Keywords

  • Edge coloring
  • Goldberg's conjecture
  • Multigraphs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Edge coloring multigraphs without small dense subsets. / Haxell, P. E.; Kierstead, Henry.

In: Discrete Mathematics, Vol. 338, No. 12, 13.07.2015, p. 2502-2506.

Research output: Contribution to journalArticle

Haxell, P. E. ; Kierstead, Henry. / Edge coloring multigraphs without small dense subsets. In: Discrete Mathematics. 2015 ; Vol. 338, No. 12. pp. 2502-2506.
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