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Graph Parameters and Ramsey Theory

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Abstract

Ramsey’s Theorem tells us that there are exactly two minimal hereditary classes containing graphs with arbitrarily many vertices: the class of complete graphs and the class of edgeless graphs. In other words, Ramsey’s Theorem characterizes the graph vertex number in terms of minimal hereditary classes where this parameter is unbounded. In the present paper, we show that a similar Ramsey-type characterization is possible for a number of other graph parameters, including neighbourhood diversity and VC-dimension.

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Acknowledgment

This work was supported by the Russian Science Foundation Grant No. 17-11-01336.

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Authors and Affiliations

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

    Vadim Lozin

  2. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Vadim Lozin

Authors
  1. Vadim Lozin
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Correspondence to Vadim Lozin .

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Editors and Affiliations

  1. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Ljiljana Brankovic

  2. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Joe Ryan

  3. McMaster University, Hamilton, Ontario, Canada

    William F. Smyth

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Lozin, V. (2018). Graph Parameters and Ramsey Theory. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-78825-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78824-1

  • Online ISBN: 978-3-319-78825-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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