J. F. Couturier
List coloring in the absence of a linear forest
Couturier, J. F.; Golovach, P. A.; Kratsch, D.; Paulusma, D.
Authors
Contributors
P. Kolman
Editor
J. Kratochvil
Editor
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 List k -Coloring problem requires in addition that every vertex u must receive a color from some given set L(u) ⊆ {1,…,k}. Let P n 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 List k -Coloring can be solved in polynomial time for graphs with no induced rP 1 + P 5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P 5. Our result is tight; we prove that for any graph H that is a supergraph of P 1 + P 5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H. We also show that List k -Coloring is fixed parameter tractable in k + r on graphs with no induced rP 1 + P 2, and that k-Coloring restricted to such graphs allows a polynomial kernel when parameterized by k. Finally, we show that List k -Coloring is fixed parameter tractable in k for graphs with no induced P 1 + P 3.
Presentation Conference Type | Conference Paper (Published) |
---|---|
Conference Name | 37th International Workshop on Graph Theoretic Concepts in Computer Science, WG 2011 |
Publication Date | Jan 1, 2011 |
Deposit Date | Dec 6, 2011 |
Pages | 119-130 |
Series Title | Lecture notes in computer science |
Series Number | 6986 |
Series ISSN | 0302-9743,1611-3349 |
Book Title | Graph-theoretic concepts in computer science, 37th International Workshop, WG 2011, Teplá Monastery, Czech Republic, June 21-24, 2011 ; revised papers. |
ISBN | 9783642258695 |
DOI | https://doi.org/10.1007/978-3-642-25870-1_12 |
Public URL | https://durham-repository.worktribe.com/output/1158308 |
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