Abstract
Finding minimal triangulations of graphs is a well-studied problem with many applications, for instance as first step for efficiently computing graph decompositions in terms of clique separators. Computing a minimal triangulation can be done in O(nm) time and much effort has been invested to improve this time bound for general and special graphs. We propose a recursive algorithm which works for general graphs and runs in linear time if the input is a claw-free graph and the length of its longest path is bounded by a fixed value k. More precisely, our algorithm runs in O(f + km) time if the input is a claw-free graph, where f is the number of fill edges added, and k is the height of the execution tree; we find all the clique minimal separators of the input graph at the same time. Our algorithm can be modified to a robust algorithm which runs within the same time bound: given a non-claw free input, it either triangulates the graph or reports a claw.
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Berry, A., Wagler, A. (2012). Triangulation and Clique Separator Decomposition of Claw-Free Graphs. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_5
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DOI: https://doi.org/10.1007/978-3-642-34611-8_5
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