English

Balancing connected colourings of graphs

Combinatorics 2023-03-31 v1

Abstract

We show that the edges of any graph GG containing two edge-disjoint spanning trees can be blue/red coloured so that the blue and red graphs are connected and the blue and red degrees at each vertex differ by at most four. This improves a result of H\"orsch. We discuss variations of the question for digraphs, infinite graphs and a computational question, and resolve two further questions of H\"orsch in the negative.

Keywords

Cite

@article{arxiv.2205.04984,
  title  = {Balancing connected colourings of graphs},
  author = {Freddie Illingworth and Emil Powierski and Alex Scott and Youri Tamitegama},
  journal= {arXiv preprint arXiv:2205.04984},
  year   = {2023}
}

Comments

23 pages, 22 figures

R2 v1 2026-06-24T11:13:19.258Z