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Exploring the complexity boundary between coloring and list-coloring. (English) Zbl 1134.68374
Faigle, U. (ed.) et al., CTW2006. Cologne-Twente Workshop on graphs and combinatorial optimization, Lambrecht, Germany, June 5–9, 2006. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 25, 41-47 (2006).
Summary: Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs, where the former admits polynomial-time algorithms but the latter is NP-complete. Our goal is to analyze the computational complexity of coloring problems lying “between” (from a computational complexity viewpoint) these two problems: precoloring extension, $$\mu$$ -coloring, and $$(\gamma, \mu)$$-coloring.
For the entire collection see [Zbl 1109.05003].

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 05C15 Coloring of graphs and hypergraphs 05C85 Graph algorithms (graph-theoretic aspects)
##### Keywords:
coloring; computational complexity; list-coloring
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##### References:
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