Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Scheduling with incompatible jobs
Discrete Applied Mathematics
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Generalized coloring for tree-like graphs
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Parameterized Complexity
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
Minimum fill-in and treewidth of split+ke and split+kv graphs
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Vertex coloring of comparability+ke and -ke
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Pathwidth and searching in parameterized threshold graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
European Journal of Combinatorics
Polynomial time and parameterized approximation algorithms for boxicity
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Data reduction for graph coloring problems
Information and Computation
| Hi-index | 0.04 |
For a family F of graphs and a nonnegative integer k, F + ke and F - ke, respectively, denote the families of graphs that can be obtained from F graphs by adding and deleting at most k edges, and F + kv denotes the family of graphs that can be made into F graphs by deleting at most k vertices.This paper is mainly concerned with the parameterized complexity of the vertex colouring problem on F + ke, F - ke and F - kv for various families F of graphs. In particular, it is shown that the vertex colouring problem is fixed-parameter tractable (linear time for each fixed k) for split + ke graphs and split - ke graphs, solvable in polynomial time for each fixed k but W[1]-hard for split + kv graphs. Furthermore, the problem is solvable in linear time for bipartite + 1v graphs and bipartite + 2e graphs but, surprisingly, NP-complete for bipartite + 2v graphs and bipartite + 3e graphs.