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Mixed Cages

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Abstract

We introduce the notion of a [z, r; g]-mixed cage. A [z, r; g]-mixed cage is a mixed graph G, z-regular by arcs, r-regular by edges, with girth g and minimum order. In this paper we prove the existence of [z, r; g]-mixed cages and exhibit families of mixed cages for some specific values. We also give lower and upper bounds for some choices of z, r and g. In particular we present the first results on [z, r; g]- mixed cages for \(z=1\) and any \(r\ge 1\) and \(g\ge 3\), and for any \(z\ge 1\), \(r=1\) and \(g=4\).

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Acknowledgements

The authors wish to thank the anonymous referees of this paper for their helpful corrections and remarks. Research supported by CONACyT-México under projects 282280, and PAPIIT-México under projects IN107218 and IN106318.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico, México

    Gabriela Araujo-Pardo & Juan José Montellano-Ballesteros

  2. Departamento de Computación, Centro de Investigación y de Estudios Avanzados del IPN, Av. Politécnico Nacional 2508, San Pedro Zacatenco, 07360, Mexico, CDMX, México

    César Hernández-Cruz

Authors
  1. Gabriela Araujo-Pardo
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  2. César Hernández-Cruz
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  3. Juan José Montellano-Ballesteros
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Correspondence to Gabriela Araujo-Pardo.

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Araujo-Pardo, G., Hernández-Cruz, C. & Montellano-Ballesteros, J.J. Mixed Cages. Graphs and Combinatorics 35, 989–999 (2019). https://doi.org/10.1007/s00373-019-02050-1

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  • DOI: https://doi.org/10.1007/s00373-019-02050-1

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