The Hamiltonian circuit problem for circle graphs in NP-complete
Information Processing Letters
The complexity of domination problems in circle graphs
Discrete Applied Mathematics
Independence and domination in polygon graphs
Discrete Applied Mathematics
Journal of Algorithms
Discrete Mathematics
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Hardness of Approximating Independent Domination in Circle Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
On the k-Colouring of Circle-Graphs
STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Colouring Circle Graphs (Extended Abstract)
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
The Monadic Second-Order Logic of Graphs: Definable Sets of Finite Graphs
WG '88 Proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Acyclic domination on bipartite permutation graphs
Information Processing Letters
Approximating the minimum clique cover and other hard problems in subtree filament graphs
Discrete Applied Mathematics
Minimum weight feedback vertex sets in circle graphs
Information Processing Letters
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
On problems without polynomial kernels
Journal of Computer and System Sciences
Dominating set is fixed parameter tractable in claw-free graphs
Theoretical Computer Science
Parameterized complexity of independence and domination on geometric graphs
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized complexity in multiple-interval graphs: domination
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
Parameterized domination in circle graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Parameterized domination in circle graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Hi-index | 0.00 |
A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs. To the best of our knowledge, nothing was known about the parameterized complexity of these problems in circle graphs. In this paper we prove the following results, which contribute in this direction: · Dominating Set, Independent Dominating Set, Connected Dominating Set, Total Dominating Set, and Acyclic Dominating Set are W[1]-hard in circle graphs, parameterized by the size of the solution. · Whereas both Connected Dominating Set and Acyclic Dominating Set are W[1]-hard in circle graphs, it turns out that Connected Acyclic Dominating Set is polynomial-time solvable in circle graphs. · If T is a given tree, deciding whether a circle graph has a dominating set isomorphic to T is NP-complete when T is in the input, and FPT when parameterized by |V(T)|. We prove that the FPT algorithm is subexponential.