Abstract
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.
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Meister, D. (2007). A Characterisation of the Minimal Triangulations of Permutation Graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_10
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DOI: https://doi.org/10.1007/978-3-540-74839-7_10
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