On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
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
Triangle-free graphs and forbidden subgraphs
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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
Graph Theory
Three Complexity Results on Coloring Pk-Free Graphs
Combinatorial Algorithms
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
Updating the complexity status of coloring graphs without a fixed induced linear forest
Theoretical Computer Science
Determining the chromatic number of triangle-free 2P3-free graphs in polynomial time
Theoretical Computer Science
List coloring in the absence of a linear forest
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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
Linear time algorithm for computing a small biclique in graphs without long induced paths
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
4-coloring H-free graphs when H is small
Discrete Applied Mathematics
List coloring in the absence of two subgraphs
Discrete Applied Mathematics
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The girth of a graph G is the length of a shortest cycle in G. For any fixed girth g ≥ 4 we determine a lower bound l(g) such that every graph with girth at least g and with no induced path on l(g) vertices is 3-colorable. In contrast, we show the existence of an integer l such that testing for 4-colorability is NP-complete for graphs with girth 4 and with no induced path on l vertices.