Strong Majority Edge-Coloring

Sylwia Antoniuk; Magdalena Prorok; Nika Salia

Strong Majority Edge-Coloring

Combinatorics 2026-06-30 v1

Authors: Sylwia Antoniuk , Magdalena Prorok , Nika Salia

Abstract

A strong majority edge-coloring of a graph is an edge-coloring in which, for every edge $e$ and every color $i$ , at most half of the edges adjacent to $e$ have color $i$ . Such a coloring exists only for graphs with no pendant path of length two, which, following Kalinowski, Kamyczura, Pil\'sniak, and Wo\'zniak, we call admissible. They proved that every admissible graph admits such a coloring with at most eight colors and conjectured that four colors always suffice. We improve the upper bound from eight to five.

Cite

@article{arxiv.2607.00212,
  title  = {Strong Majority Edge-Coloring},
  author = {Sylwia Antoniuk and Magdalena Prorok and Nika Salia},
  journal= {arXiv preprint arXiv:2607.00212},
  year   = {2026}
}