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
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
How to Use the Minimal Separators of a Graph for its Chordal Triangulation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Mixed Search Number of Permutation Graphs
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Edge Search Number of Cographs in Linear Time
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Characterizing and computing minimal cograph completions
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
Edge search number of cographs
Discrete Applied Mathematics
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A chordal graph H is a triangulation of a graph G, if H is obtained by adding edges to G. If no proper subgraph of H is a triangulation of G, then H is a minimal triangulation of G. A potential maximal clique of G is a set of vertices that induces a maximal clique in a minimal triangulation of G. We will characterise the potential maximal cliques of permutation graphs and give a characterisation of minimal triangulations of permutation graphs in terms of sets of potential maximal cliques. This results in linear-time algorithms for computing treewidth and minimum fill-in for permutation graphs.