A survey of graph layout problems
ACM Computing Surveys (CSUR)
Computing the Treewidth and the Minimum Fill-in with the Modular Decomposition
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A Linear Time Algorithm for Enumerating All the Minimum and Minimal Separators of a Chordal Graph
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Generating All the Minimal Separators of a Graph
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Efficient Analysis of Graphs with Small Minimal Separators
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Computing Optimal Linear Layouts of Trees in Linear Time
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
A Linear-Time Algorithm for Constructing an Optimal Node-Search Strategy of a Tree
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Approximating the treewidth of AT-free graphs
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors
Journal of Computer and System Sciences
The first order definability of graphs with separators via the Ehrenfeucht game
Theoretical Computer Science - Game theory meets theoretical computer science
Node-searching problem on block graphs
Discrete Applied Mathematics
Mixed Search Number of Permutation Graphs
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Discrete Applied Mathematics
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Edge Search Number of Cographs in Linear Time
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Pathwidth is NP-Hard for Weighted Trees
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Reconfiguration of the routing in WDM networks with two classes of services
ONDM'09 Proceedings of the 13th international conference on Optical Network Design and Modeling
Approximating the treewidth of AT-free graphs
Discrete Applied Mathematics
On the treewidth and pathwidth of biconvex bipartite graphs
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A characterisation of the minimal triangulations of permutation graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Treewidth and minimum fill-in on permutation graphs in linear time
Theoretical Computer Science
Treewidth computations II. Lower bounds
Information and Computation
Algorithms and complexity results for graph-based pursuit evasion
Autonomous Robots
Generation of graphs with bounded branchwidth
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Graph searching and search time
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Computing treewidth and minimum fill-in for permutation graphs in linear time
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Computing branchwidth via efficient triangulations and blocks
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Edge search number of cographs
Discrete Applied Mathematics
Restricted vertex multicut on permutation graphs
Discrete Applied Mathematics
Approximate search strategies for weighted trees
Theoretical Computer Science
Computing K-terminal reliability of d-trapezoid graphs
Information Processing Letters
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In this paper, we show that the treewidth and pathwidth of a permutation graph can be computed in polynomial time. In fact we show that, for permutation graphs, the treewidth and pathwidth are equal. These results make permutation graphs one of the few nontrivial graph classes for which, at the moment, treewidth is known to be computable in polynomial time. Our algorithm, which decides whether the treewidth (pathwidth) is at most some given integer $k$, can be implemented to run in $O(nk)$ time when the matching diagram is given. We show that this algorithm can easily be adapted to compute the pathwidth of a permutation graph in $O(nk)$ time, where $k$ is the pathwidth.