43. chen.shan:26:exploring#
Exploring the world of edge-chromatic 3-critical graphs
Le Chen and Songling Shan
Abstract: A graph \(G\) with maximum degree \(\Delta\) is \(\Delta\)-critical if it is connected, satisfies \(\chi'(G)=\Delta+1\), and the deletion of any edge reduces its chromatic index to \(\Delta\). This preprint studies nontrivial 3-critical graphs, combining computer-assisted enumeration with structural characterization.
Preprint Codes & data: GitHub repository, project website, Zenodo (DOI)
[CS26] Le Chen & Songling Shan (2026) ‘Exploring the world of edge-chromatic 3-critical graphs’, preprint arXiv:2606.27131, 31 pages
@article{chen.shan:26:exploring,
title = {Exploring the world of edge-chromatic 3-critical graphs},
author = {Le Chen and Songling Shan},
year = {2026},
month = {June},
journal = {preprint arXiv:2606.27131, 31 pages},
url = {https://arxiv.org/abs/2606.27131}
}