Balancing connected colourings of graphs
Combinatorics
2023-03-31 v1
Abstract
We show that the edges of any graph 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.
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