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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/15059

Title: Polynomial-time algorithms for Subgraph Isomorphism in small graph classes of perfect graphs
Authors: Konagaya, Matsuo
Otachi, Yota
Uehara, Ryuhei
Keywords: sugbraph isomorphism
graph class
polynomial time algorithm
Issue Date: 2016-02-23
Publisher: Elsevier
Magazine name: Discrete Applied Mathematics
Volume: 199
Start page: 37
End page: 45
DOI: 10.1016/j.dam.2015.01.040
Abstract: Given two graphs, Subgraph Isomorphism is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second graph (the pattern graph). This problem is NP-complete for very restricted graph classes such as connected proper interval graphs. Only a few cases are known to be polynomial-time solvable even if we restrict the graphs to be perfect. For example, if both graphs are co-chain graphs, then the problem can besolved in linear time. In this paper, we present a polynomial-time algorithm for the case where the base graphsare chordal graphs and the pattern graphs are co-chain graphs. We also present a linear-time algorithm for the case where the base graphs are trivially perfect graphs and the pattern graphs are threshold graphs. These results answer some of the open questions of Kijima et al. [DiscreteMath. 312, pp. 3164–3173, 2012]. To present a complexity contrast, we then show that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete.
Rights: Copyright (C)2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] 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 Matsuo Konagaya, Yota Otachi, and Ryuhei Uehara, Discrete Applied Mathematics, 199, 2016, 37-45, http://dx.doi.org/10.1016/j.dam.2015.01.040
URI: http://hdl.handle.net/10119/15059
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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