Colouring vertices of triangle-free graphs

Authors:
Konrad Dabrowski;Vadim Lozin;Rajiv Raman;Bernard Ries
Affiliations:
DIMAP, University of Warwick, Coventry, UK;DIMAP, University of Warwick, Coventry, UK;DIMAP, University of Warwick, Coventry, UK;DIMAP, University of Warwick, Coventry, UK
Venue:
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Year:
2010

Citing 17
Cited 6

On the NP-completeness of the k-colorability problem for triangle-free graphs

Discrete Mathematics
Induced trees in graphs of large chromatic number

Journal of Graph Theory
Upper bounds to the clique width of graphs

Discrete Applied Mathematics
The complexity of coloring graphs without long induced paths

Acta Cybernetica
A 4-colour problem for dense triangle-free graphs

Discrete Mathematics
Three-colourbility and forbidden subgraphs. II: polynomial algorithms

Discrete Mathematics
Bipartite graphs without a skew star

Discrete Mathematics
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 3-Colorability Problem on Graphs with Maximum Degree Four

SIAM Journal on 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
On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree

SIAM Journal on Discrete Mathematics
Note: On the complexity of 4-coloring graphs without long induced paths

Theoretical Computer Science
Recent developments on graphs of bounded clique-width

Discrete Applied Mathematics
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

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
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
On the parameterized complexity of coloring graphs in the absence of a linear forest

Journal of Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

The VERTEX COLOURING problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it remains NP-complete even if we additionally exclude a graph F which is not a forest. We study the computational complexity of the problem in (K3, F)-free graphs with F being a forest. From known results it follows that for any forest F on 5 vertices the VERTEX COLOURING problem is polynomial-time solvable in the class of (K3, F)-free graphs. In the present paper, we show that the problem is also polynomial-time solvable in many classes of (K3, F)-free graphs with F being a forest on 6 vertices.