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On the Number of Heterochromatic Trees in Nice and Beautiful Colorings of Complete Graphs

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Abstract

We introduce classes of edge-colourings of the complete graph—that we call nice and beautiful—and study how many heterochromatic spanning trees appear under such colourings. We prove that if the colouring is nice, there is at least a quadratic number of different heterochromatic trees; and if the colouring is beautiful there is an exponential number of different such trees.

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Funding

Research partially supported by PAPIIT-México project IN108121 and CONACyT-México project A1-S-12891.

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Authors and Affiliations

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

    Juan José Montellano-Ballesteros & Ricardo Strausz

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, Mexico City, Mexico

    Eduardo Rivera-Campo

Authors
  1. Juan José Montellano-Ballesteros
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  2. Eduardo Rivera-Campo
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  3. Ricardo Strausz
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Correspondence to Juan José Montellano-Ballesteros.

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Montellano-Ballesteros, J.J., Rivera-Campo, E. & Strausz, R. On the Number of Heterochromatic Trees in Nice and Beautiful Colorings of Complete Graphs. Graphs and Combinatorics 38, 12 (2022). https://doi.org/10.1007/s00373-021-02436-0

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  • DOI: https://doi.org/10.1007/s00373-021-02436-0

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