Abstract
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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Meister, D. (2005). Computing Treewidth and Minimum Fill-In for Permutation Graphs in Linear Time. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_9
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DOI: https://doi.org/10.1007/11604686_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31000-6
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