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Combinatorics and Algorithms for Quasi-chain Graphs

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Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

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Abstract

The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. The latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced subgraphs, etc. The class of quasi-chain graphs is substantially more complex. In particular, this class is not well-quasi-ordered by induced subgraphs, and the clique-width is not bounded in it. In the present paper, we show that the universe of quasi-chain graphs is at least as complex as the universe of permutations by establishing a bijection between the class of all permutations and a subclass of quasi-chain graphs. This implies, in particular, that the induced subgraph isomorphism problem is NP-complete for quasi-chain graphs. On the other hand, we propose a decomposition theorem for quasi-chain graphs that implies an implicit representation for graphs in this class and efficient solutions for some algorithmic problems that are generally intractable.

This work was supported by the Russian Science Foundation Grant No. 21-11-00194.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Bogdan Alecu & Vadim Lozin

  2. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, Suzhou, 215123, China

    Aistis Atminas

  3. Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, 136 Rodionova Str., 603093, Nizhny Novgorod, Russia

    Dmitriy Malyshev

  4. National Research Lobachevsky State University of Nizhny Novgorod, 23 Gagarina Ave., Nizhny Novgorod, 603950, Russia

    Dmitriy Malyshev

Authors
  1. Bogdan Alecu
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  2. Aistis Atminas
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  3. Vadim Lozin
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  4. Dmitriy Malyshev
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Corresponding author

Correspondence to Vadim Lozin .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Ottawa, Ottawa, ON, Canada

    Lucia Moura

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Alecu, B., Atminas, A., Lozin, V., Malyshev, D. (2021). Combinatorics and Algorithms for Quasi-chain Graphs. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_4

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  • DOI: https://doi.org/10.1007/978-3-030-79987-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

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