Discussiones Mathematicae Graph Theory 33(1) (2013)
231-242
DOI: https://doi.org/10.7151/dmgt.1660
Dedicated to Mietek Borowiecki on the occasion of his seventieth birthday
Choice-perfect Graphs
Zsolt Tuza
Alfréd Rényi Institute of Mathematics |
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 → ∪v ∈ 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 number equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, respectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.
Keywords: graph coloring, list coloring, choice-perfect graph
2010 Mathematics Subject Classification: 05C15, 05C17, 05C75.
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Received 28 April 2012
Revised 5 September 2012
Accepted 5 September 2012
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