J. Couturier
List Coloring in the Absence of a Linear Forest
Couturier, J.; Golovach, P.A.; Kratsch, D.; Paulusma, D.
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.
Citation
Couturier, J., Golovach, P., Kratsch, D., & Paulusma, D. (2015). List Coloring in the Absence of a Linear Forest. Algorithmica, 71(1), 21-35. https://doi.org/10.1007/s00453-013-9777-0
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 30, 2013 |
Online Publication Date | Apr 6, 2013 |
Publication Date | Jan 1, 2015 |
Deposit Date | Apr 15, 2013 |
Publicly Available Date | Apr 17, 2013 |
Journal | Algorithmica |
Print ISSN | 0178-4617 |
Electronic ISSN | 1432-0541 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 71 |
Issue | 1 |
Pages | 21-35 |
DOI | https://doi.org/10.1007/s00453-013-9777-0 |
Public URL | https://durham-repository.worktribe.com/output/1487502 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-013-9777-0.
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