On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
Generalized coloring for tree-like graphs
Discrete Applied Mathematics
The complexity of coloring graphs without long induced paths
Acta Cybernetica
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Complexity of Coloring Graphs without Forbidden Induced Subgraphs
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
3-Colorability ∈ P for P6-free graphs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Vertex Colouring and Forbidden Subgraphs – A Survey
Graphs and Combinatorics
Note: On the complexity of 4-coloring graphs without long induced paths
Theoretical Computer Science
Graph Theory
Three Complexity Results on Coloring Pk-Free Graphs
Combinatorial Algorithms
A Certifying Algorithm for 3-Colorability of P5-Free Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Deciding k-Colorability of P 5-Free Graphs in Polynomial Time
Algorithmica - Including a Special Section on Genetic and Evolutionary Computation; Guest Editors: Benjamin Doerr, Frank Neumann and Ingo Wegener
Colouring vertices of triangle-free graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Parameterized Complexity
Coloring graphs without short cycles and long induced paths
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
4-coloring h-free graphs when h is small
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
On the parameterized complexity of coloring graphs in the absence of a linear forest
Journal of Discrete Algorithms
4-coloring H-free graphs when H is small
Discrete Applied Mathematics
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Colouring of graphs with Ramsey-type forbidden subgraphs
Theoretical Computer Science
List coloring in the absence of two subgraphs
Discrete Applied Mathematics
Coloring graphs without short cycles and long induced paths
Discrete Applied Mathematics
| Hi-index | 0.00 |
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, Kami$#324;ski, 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. We also show that Listk-Coloring is fixed parameter tractable in k+r on graphs with no induced rP1+P2, and that k-Coloring restricted to such graphs allows a polynomial kernel when parameterized by k. Finally, we show that Listk-Coloring is fixed parameter tractable in k for graphs with no induced P1+P3.