A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k≤3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we prove that the problem is fixed parameter tractable on P 5-free graphs when parameterized by k. This graph class contains the well known and widely studied class of cographs. Our result is surprising since the parameterized complexity of k-coloring is still open on P 5-free graphs. To give a complete picture, we show that the problem remains NP-hard on P 5-free graphs when k is a part of the input. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Golovach, P. A., & Heggernes, P. (2009). Choosability of P 5-free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5734 LNCS, pp. 382–391). https://doi.org/10.1007/978-3-642-03816-7_33
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