Abstract
In this paper, we present the clique arrangement \(\mathcal{A}\)(G) for a chordal graph G to describe the intersections between the maximal cliques of G more precisely than in clique trees or related concepts. In particular, the node set of \(\mathcal{A}\)(G) consists of all intersections of maximal cliques of G. In \(\mathcal{A}\)(G), there is an arc from a node X to a node Z, if X is a subset of Z and there is no node Y, that is a superset of X and a subset of Z.
We provide a new characterization of strongly chordal graphs in terms of forbidden cyclic structures in the corresponding clique arrangements and we show how to compute the clique arrangement of a strongly chordal graph efficiently.
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Nevries, R., Rosenke, C. (2013). Characterizing and Computing the Structure of Clique Intersections in Strongly Chordal Graphs. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 2013. Lecture Notes in Computer Science, vol 8165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45043-3_33
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DOI: https://doi.org/10.1007/978-3-642-45043-3_33
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