On the number of heterochromatic trees in nice and beautiful colourings of complete graphs
Juan José Montellano‐Ballesteros, Eduardo Rivera‐Campo, Ricardo Strausz · arXiv (Cornell University) · 2021
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.