Circular chromatic index of small graphs
Combinatorics
2026-03-11 v1 Discrete Mathematics
Abstract
We systematically determine circular chromatic index of small graphs and multigraphs with maximum degree , , (and also their number for a given small order). We construct several infinite families of such graphs with circular chromatic index in the set , . Our results refute edge-connectivity variants of the ``Upper Gap Conjecture'' (about the non-existence of graphs with circular chromatic index just below ).
Cite
@article{arxiv.2603.08822,
title = {Circular chromatic index of small graphs},
author = {Ján Mazák and Filip Zrubák},
journal= {arXiv preprint arXiv:2603.08822},
year = {2026}
}