Decompositions into isomorphic rainbow spanning trees
Combinatorics
2020-03-09 v2
Abstract
A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring of a sufficiently large complete graph , there exists a decomposition of into isomorphic rainbow spanning trees. This settles conjectures of Brualdi--Hollingsworth (from 1996) and Constantine (from 2002) for large graphs.
Cite
@article{arxiv.1903.04262,
title = {Decompositions into isomorphic rainbow spanning trees},
author = {Stefan Glock and Daniela Kühn and Richard Montgomery and Deryk Osthus},
journal= {arXiv preprint arXiv:1903.04262},
year = {2020}
}
Comments
Version accepted to appear in JCTB