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
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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
Restricted vertex multicut on permutation graphs
Discrete Applied Mathematics
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A minimal triangulation of a graph is a chordal graph obtained from adding an inclusion-minimal set of edges to the graph. For permutation graphs, i.e., graphs that are both comparability and cocomparability graphs, it is known that minimal triangulations are interval graphs. We (negatively) answer the question whether every interval graph is a minimal triangulation of a permutation graph. We give a non-trivial characterisation of the class of interval graphs that are minimal triangulations of permutation graphs and obtain as a surprising result that only "a few" interval graphs are minimal triangulations of permutation graphs.