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
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)
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
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
Updating the complexity status of coloring graphs without a fixed induced linear forest
Theoretical 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
Maximum regular induced subgraphs in 2P3-free graphs
Theoretical Computer Science
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 | 5.23 |
Let 2P"3 denote the disjoint union of two paths on three vertices. A graph G that has no subgraph isomorphic to a graph H is called H-free. The Vertex Coloring problem is the problem to determine the chromatic number of a graph. Its computational complexity for triangle-free H-free graphs has been classified for every fixed graph H on at most 6 vertices except for the case H=2P"3. This remaining case is posed as an open problem by Dabrowski, Lozin, Raman and Ries. We solve their open problem by showing polynomial-time solvability.