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List coloring in the absence of a linear forest.

Couturier, J. and Golovach, P.A. and Kratsch, D. and Paulusma, Daniel (2015) 'List coloring in the absence of a linear forest.', Algorithmica., 71 (1). pp. 21-35.

Abstract

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/s00453-013-9777-0
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-013-9777-0.
Date accepted:30 March 2013
Date deposited:17 April 2013
Date of first online publication:06 April 2013
Date first made open access:No date available

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