English

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 K2nK_{2n}, there exists a decomposition of K2nK_{2n} into isomorphic rainbow spanning trees. This settles conjectures of Brualdi--Hollingsworth (from 1996) and Constantine (from 2002) for large graphs.

Keywords

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

R2 v1 2026-06-23T08:04:09.835Z