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Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs

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Theory and Applications of Models of Computation (TAMC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8402))

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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 be solved in linear time.

In this paper, we present a polynomial-time algorithm for the case where the base graphs are 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. [Discrete Math. 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.

Partially supported by JSPS KAKENHI Grant Numbers 23500013, 25730003, and by MEXT KAKENHI Grant Number 24106004.

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Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, 923-1292, Japan

    Matsuo Konagaya, Yota Otachi & Ryuhei Uehara

Authors
  1. Matsuo Konagaya
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  2. Yota Otachi
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  3. Ryuhei Uehara
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, College of Engineering, Anna University, Chennai, 600 025, Chennai, India

    T. V. Gopal

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 208016, Kanpur, India

    Manindra Agrawal

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Zhongguancun, Haidian District, 100190, Beijing, China

    Angsheng Li

  4. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

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Konagaya, M., Otachi, Y., Uehara, R. (2014). Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_15

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  • DOI: https://doi.org/10.1007/978-3-319-06089-7_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06088-0

  • Online ISBN: 978-3-319-06089-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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