A Complete Characterisation of the Linear Clique-Width of Path Powers

Authors:
Pinar Heggernes;Daniel Meister;Charis Papadopoulos
Affiliations:
Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway;Department of Mathematics, University of Ioannina, Greece
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

Citing 18
Cited 3

Handle-rewriting hypergraph grammars

Journal of Computer and System Sciences
Upper bounds to the clique width of graphs

Discrete Applied Mathematics
On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic

Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Edge dominating set and colorings on graphs with fixed clique-width

Discrete Applied Mathematics
On the Clique-Width of Graphs in Hereditary Classes

ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)

LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree

SIAM Journal on Discrete Mathematics
On the Relationship Between Clique-Width and Treewidth

SIAM Journal on Computing
New Graph Classes of Bounded Clique-Width

Theory of Computing Systems
Clique-width minimization is NP-hard

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the relationship between NLC-width and linear NLC-width

Theoretical Computer Science
Clique-Width for 4-Vertex Forbidden Subgraphs

Theory of Computing Systems
The relative clique-width of a graph

Journal of Combinatorial Theory Series B
Clique-width: on the price of generality

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
From Tree-Width to Clique-Width: Excluding a Unit Interval Graph

ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The NLC-width and clique-width for powers of graphs of bounded tree-width

Discrete Applied Mathematics
Graphs of linear clique-width at most 3

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Computing graph polynomials on graphs of bounded clique-width

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science

Computing the Clique-width of large path powers in linear time via a new characterisation of clique-width

CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Exploiting restricted linear structure to cope with the hardness of clique-width

TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Characterising the linear clique-width of a class of graphs by forbidden induced subgraphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A k -path power is the k -power graph of a simple path of arbitrary length. Path powers form a non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a constant, and no polynomial-time algorithm is known for computing their clique-width or linear clique-width. We show that k -path powers above a certain size have linear clique-width exactly k + 2, providing the first complete characterisation of the linear clique-width of a graph class of unbounded clique-width. Our characterisation results in a simple linear-time algorithm for computing the linear clique-width of all path powers.