The complexity of colouring problems on dense graphs
Theoretical Computer Science
Coloring perfect (K4-e)-free graphs
Journal of Combinatorial Theory Series B
A reduction procedure for coloring perfect K4-free graphs
Journal of Combinatorial Theory Series B
Information Processing Letters
Applications of edge coloring of multigraphs to vertex coloring of graphs
Discrete Mathematics - Graph colouring and variations
A characterization of graphs without long induced paths
Journal of Graph Theory
A strengthening of Ben Rebea's lemma
Journal of Combinatorial Theory Series B
The Ramsey number R(3, t) has order of magnitude t2/log t
Random Structures & Algorithms
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
Dominating sets with small clique covering number
Journal of Graph Theory
3-coloring in time 0(1.3446^n): a no-MIS algorithm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Graph Theory With Applications
Graph Theory With Applications
Journal of Graph Theory
Triangle-free graphs and forbidden subgraphs
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
3-Colorability ∈ P for P6-free graphs
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Note: On the complexity of 4-coloring graphs without long induced paths
Theoretical Computer Science
NP-hard graph problems and boundary classes of graphs
Theoretical Computer Science
First-Fit coloring of {P5,K4-e}-free graphs
Discrete Applied Mathematics
Colouring vertices of triangle-free graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Clique-width for four-vertex forbidden subgraphs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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In this paper we study the chromatic number for graphs with forbidden induced subgraphs. We focus our interest on graph classes (defined in terms of forbidden induced subgraphs) for which the question of 3-colourability can be decided in polynomial time and, if so, a proper 3-colouring can be determined also in polynomial time. Note that the 3-colourability decision problem is a well-known NP-complete problem, even for special graph classes, e.g. triangle-free and K1,5-free (Discrete Math. 162 (1-3) (1996) 313). Therefore, it is unlikely that there exists a polynomial algorithm deciding whether there exists a 3-colouring of a given graph in general. We present three different approaches to reach our goal. The first approach is purely a structural analysis of the graph class in consideration; the second one is a structural analysis of only the non-perfect K4-free members of the considered graph class; finally the last approach is based on propositional logic and bounded dominating subgraphs.