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このアイテムの引用には次の識別子を使用してください: http://hdl.handle.net/10119/9180

タイトル: Laminar Structure of Ptolemaic Graphs with Applications
著者: Uehara, Ryuhei
Uno, Yushi
キーワード: Algorithmic graph theory
Data structures
γ-acyclicity
Hamiltonian cycle
Intersection model
Ptolemaic graphs
発行日: 2008-10-23
出版者: Elsevier
誌名: Discrete Applied Mathematics
巻: 157
号: 7
開始ページ: 1533
終了ページ: 1543
DOI: 10.1016/j.dam.2008.09.006
抄録: Ptolemaic graphs are those satisfying the Ptolemaic inequality for any four vertices. The graph class coincides with the intersection of chordal graphs and distance hereditary graphs. It can also be seen as a natural generalization of block graphs (and hence trees). In this paper, we first state a laminar structure of cliques, which leads to its canonical tree representation. This result is a translation of γ-acyclicity which appears in the context of relational database schemes. The tree representation gives a simple intersection model of ptolemaic graphs, and it is constructed in linear time from a perfect elimination ordering obtained by the lexicographic breadth first search. Hence the recognition and the graph isomorphism for ptolemaic graphs can be solved in linear time. Using the tree representation, we also give an efficient algorithm for the Hamiltonian cycle problem.
Rights: NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Ryuhei Uehara and Yushi Uno, Discrete Applied Mathematics, 157(7), 2008, 1533-1543, http://dx.doi.org/10.1016/j.dam.2008.09.006
URI: http://hdl.handle.net/10119/9180
資料タイプ: author
出現コレクション:b10-1. 雑誌掲載論文 (Journal Articles)

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