Scheduling with incompatible jobs
Discrete Applied Mathematics
Graph classes: a survey
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
Parameterized complexity of vertex colouring
Discrete Applied Mathematics
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
Invitation to data reduction and problem kernelization
ACM SIGACT News
Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
On problems without polynomial kernels
Journal of Computer and System Sciences
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
On the hardness of losing width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
European Journal of Combinatorics
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
On the Hardness of Losing Width
Theory of Computing Systems
Hi-index | 0.00 |
This paper studies the kernelization complexity of graph coloring problems, with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink instances of coloring problems, in terms of the chosen parameter. It is well known that deciding 3-colorability is already NP-complete, hence parameterizing by the requested number of colors is not fruitful. Instead, we pick up on a research thread initiated by Cai (DAM, 2003) who studied coloring problems parameterized by the modification distance of the input graph to a graph class on which coloring is polynomial-time solvable; for example parameterizing by the number k of vertex-deletions needed to make the graph chordal. We obtain various upper and lower bounds for kernels of such parameterizations of q-Coloring, complementing Cai's study of the time complexity with respect to these parameters.