Choice-perfect graphs

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1 Citation (Scopus)

Abstract

Given a graph G = (V,E) and a set Lv of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring φ : V →Uv∈V Lv such that φ(v) ∈ Lv for all v ∈ V and φ(u) ≠ φ(v) for all uv ∈ E. If such a φ exists, G is said to be list colorable. The choice number of G is the smallest natural number k for which G is list colorable whenever each list contains at least k colors. In this note we initiate the study of graphs in which the choice num- ber equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, re- spectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.

Original languageEnglish
Pages (from-to)231-242
Number of pages12
JournalDiscussiones Mathematicae - Graph Theory
Volume33
Issue number1
DOIs
Publication statusPublished - Apr 24 2013

Keywords

  • Choice-perfect graph
  • Graph coloring
  • List coloring

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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