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arXiv · 2106.02905

On the number of heterochromatic trees in nice and beautiful colourings of complete graphs

Juan José Montellano-Ballesteros·Eduardo Rivera-Campo·Ricardo Strausz
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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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Juan José Montellano-Ballesteros, Eduardo Rivera-Campo, Ricardo Strausz. 2021-11-16. On the number of heterochromatic trees in nice and beautiful colourings of complete graphs. https://arxiv.org/abs/2106.02905

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