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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2019: Graph-Theoretic Concepts in Computer Science pp 379–391Cite as

Minimal Separators in Graph Classes Defined by Small Forbidden Induced Subgraphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11789))

Abstract

Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially bounded number of minimal separators. Several well-known graph classes have this property, including chordal graphs, permutation graphs, circular-arc graphs, and circle graphs. We perform a systematic study of the question which classes of graphs defined by small forbidden induced subgraphs have a polynomially bounded number of minimal separators. We focus on sets of forbidden induced subgraphs with at most four vertices and obtain an almost complete dichotomy, leaving open only two cases.

The work is supported in part by the Slovenian Research Agency (I0-0035, research program P1-0285 and research projects J1-9110, N1-0102, and a Young Researchers grant). Part of the work was done while M. M. was visiting Osaka Prefecture University in Japan, under the operation Mobility of Slovene higher education teachers 2018–2021, co-financed by the Republic of Slovenia and the European Union under the European Social Fund.

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Authors and Affiliations

  1. University of Primorska, IAM, Muzejski trg 2, 6000, Koper, Slovenia

    Martin Milanič & Nevena Pivač

  2. University of Primorska, FAMNIT, Glagoljaška 8, 6000, Koper, Slovenia

    Martin Milanič

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  1. Martin Milanič
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  2. Nevena Pivač
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Correspondence to Nevena Pivač .

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Editors and Affiliations

  1. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Ignasi Sau

  2. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Dimitrios M. Thilikos

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Milanič, M., Pivač, N. (2019). Minimal Separators in Graph Classes Defined by Small Forbidden Induced Subgraphs. In: Sau, I., Thilikos, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2019. Lecture Notes in Computer Science(), vol 11789. Springer, Cham. https://doi.org/10.1007/978-3-030-30786-8_29

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  • DOI: https://doi.org/10.1007/978-3-030-30786-8_29

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  • Online ISBN: 978-3-030-30786-8

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