The complexity of colouring problems on dense graphs
Theoretical Computer Science
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
The complexity of coloring graphs without long induced paths
Acta Cybernetica
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
Coloring graphs without short cycles and long induced paths
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
List coloring in the absence of a linear forest
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
On the parameterized complexity of coloring graphs in the absence of a linear forest
Journal of Discrete Algorithms
Coloring graphs characterized by a forbidden subgraph
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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The k -Coloring problem is to test whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. If a graph G does not contain a graph H as an induced subgraph, then G is called H -free. For any fixed graph H on at most 6 vertices, it is known that 3-Coloring is polynomial-time solvable on H -free graphs whenever H is a linear forest and NP-complete otherwise. By solving the missing case P 2 +P 3 , we prove the same result for 4-Coloring provided that H is a fixed graph on at most 5 vertices.