English

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 44, 55, 66 (and also their number for a given small order). We construct several infinite families of such graphs with circular chromatic index in the set {Δ+1/2,Δ+2/3,Δ+3/4\{\Delta + 1/2, \Delta + 2/3, \Delta + 3/4, Δ+1}\Delta + 1\}. Our results refute edge-connectivity variants of the ``Upper Gap Conjecture'' (about the non-existence of graphs with circular chromatic index just below Δ+1\Delta + 1).

Keywords

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}
}
R2 v1 2026-07-01T11:11:01.078Z