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2013 | 33 | 1 | 231-242

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Choice-Perfect Graphs


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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 → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= 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.

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  • Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences H–1053 Budapest, Reáltanoda u. 13–15, Hungary
  • Department of Computer Science and Systems Technology University of Pannonia H–8200 Veszprém, Egyetem u. 10, Hungary


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