Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
Treewidth and Pathwidth of Permutation Graphs
SIAM Journal on Discrete Mathematics
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
On treewidth and minimum fill-in of asteroidal triple-free graphs
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
Listing all potential maximal cliques of a graph
Theoretical Computer Science
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Discrete Applied Mathematics
Optimal linear arrangement of interval graphs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Restricted vertex multicut on permutation graphs
Discrete Applied Mathematics
| Hi-index | 5.23 |
Permutation graphs form a well-studied subclass of cocomparability graphs. Permutation graphs are the cocomparability graphs whose complements are also cocomparability graphs. A triangulation of a graph G is a graph H that is obtained by adding edges to G to make it chordal. If no triangulation of G is a proper subgraph of H then H is called a minimal triangulation. The main theoretical result of the paper is a characterisation of the minimal triangulations of a permutation graph, that also leads to a succinct and linear-time computable representation of the set of minimal triangulations. We apply this representation to devise linear-time algorithms for various minimal triangulation problems on permutation graphs, in particular, we give linear-time algorithms for computing treewidth and minimum fill-in on permutation graphs.