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