Disconnected colors in generalized Gallai-colorings

Shinya Fujita, A. Gyárfás, Colton Magnant, Ákos Seress

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Gallai-colorings of complete graphs - edge colorings such that no triangle is colored with three distinct colors - occur in various contexts such as the theory of partially ordered sets (in Gallai's original paper), information theory and the theory of perfect graphs. A basic property of Gallai-colorings with at least three colors is that at least one of the color classes must span a disconnected graph. We are interested here in whether this or a similar property remains true if we consider colorings that do not contain a rainbow copy of a fixed graph F. We show that such graphs F are very close to bipartite graphs, namely, they can be made bipartite by the removal of at most one edge. We also extend Gallai's property for two infinite families and show that it also holds when F is a path with at most six vertices.

Original languageEnglish
Pages (from-to)104-114
Number of pages11
JournalJournal of Graph Theory
Volume74
Issue number1
DOIs
Publication statusPublished - Sep 2013

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Colouring
Graph in graph theory
Perfect Graphs
Edge Coloring
Graph Coloring
Partially Ordered Set
Information Theory
Complete Graph
Bipartite Graph
Triangle
Distinct
Path
Color
Class
Family
Context

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Disconnected colors in generalized Gallai-colorings. / Fujita, Shinya; Gyárfás, A.; Magnant, Colton; Seress, Ákos.

In: Journal of Graph Theory, Vol. 74, No. 1, 09.2013, p. 104-114.

Research output: Contribution to journalArticle

Fujita, Shinya ; Gyárfás, A. ; Magnant, Colton ; Seress, Ákos. / Disconnected colors in generalized Gallai-colorings. In: Journal of Graph Theory. 2013 ; Vol. 74, No. 1. pp. 104-114.
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