Oriented list colorings of graphs

Zs Tuza, M. Voigt

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A 2-assignment on a graph G= (V,E) is a collection of pairs L(v) of allowed colors specified for all vertices v ∈ V. The graph G (with at least one edge) .is said to have oriented choice number 2 if it admits an orientation which satisfies the following property: For every 2-assignment there exists a choice c(v) ∈L(v) for all v ∈V such that (i) if c(v)=c(w), then vW ∈ E, and (ii) for every ordered pair (a,b) of colors, if some edge oriented from color a to color b occurs, then no edge is oriented from color b to color a. In this paper we characterize the following subclasses of graphs of oriented choice number 2: matchings; connected graphs; graphs containing at least one cycle. In particular, the first result (which implies that the matching with 11 edges has oriented choice number 2) proves a conjecture of Sali and Simonyi

Original languageEnglish
Pages (from-to)217-229
Number of pages13
JournalJournal of Graph Theory
Volume36
Issue number4
DOIs
Publication statusPublished - Apr 2001

Keywords

  • Directed graphs
  • List colorings
  • Oriented colorings

ASJC Scopus subject areas

  • Geometry and Topology

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