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Graph Functionality

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Graph-Theoretic Concepts in Computer Science (WG 2019)

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

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Abstract

In the present paper, we introduce the notion of graph functionality, which generalizes simultaneously several other graph parameters, such as degeneracy or clique-width, in the sense that bounded degeneracy or bounded clique-width imply bounded functionality. Moreover, we show that this generalization is proper by revealing classes of graphs of unbounded degeneracy and clique-width, where functionality is bounded by a constant. We also prove that bounded functionality implies bounded VC-dimension, i.e. graphs of bounded VC-dimension extend graphs of bounded functionality, and this extension also is proper.

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Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, UK

    Bogdan Alecu & Vadim Lozin

  2. Department of Mathematics, London School of Economics, London, UK

    Aistis Atminas

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

Correspondence to Vadim Lozin .

Editor information

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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Alecu, B., Atminas, A., Lozin, V. (2019). Graph Functionality. 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_11

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  • DOI: https://doi.org/10.1007/978-3-030-30786-8_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30785-1

  • Online ISBN: 978-3-030-30786-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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