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• W1646789727 abstract "In this paper, we use the new notion of clique arrangements to suggest that leaf powers are a natural special case of strongly chordal graphs. The clique arrangement $$mathcal{A}(G)$$ of a chordal graph G is a directed graph that represents the intersections between maximal cliques of G by nodes and the inclusion relation of these vertex subsets by arcs. Recently, strongly chordal graphs have been characterized as the graphs that have a clique arrangement without bad k-cycles for $$k ge 3$$ . The class $$mathcal{L}_k$$ of k-leaf powers consists of graphs $$G=(V,E)$$ that have a k-leaf root, that is, a tree T with leaf set V, where $$xy in E$$ if and only if the T-distance between x and y is at most k. Structural characterizations and linear time recognition algorithms have been found for 2-, 3-, 4-, and, to some extent, 5-leaf powers, and it is known that the union of all k-leaf powers, that is, the graph class $$mathcal{L}= bigcup _{k=2}^infty mathcal{L}_k$$ , forms a proper subclass of strongly chordal graphs. Despite that, no essential progress has been made lately. In this paper, we characterize the subclass of strongly chordal graphs that have a clique arrangement without certain bad 2-cycles and show that $$mathcal{L}$$ is contained in that class." @default.
• W1646789727 created "2016-06-24" @default.
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• W1646789727 date "2016-05-09" @default.
• W1646789727 modified "2023-09-27" @default.
• W1646789727 title "Towards a Characterization of Leaf Powers by Clique Arrangements" @default.
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• W1646789727 doi "https://doi.org/10.1007/s00373-016-1707-x" @default.
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