English

Vertex-coloring graphs with 4-edge-weightings

Combinatorics 2023-05-04 v3

Abstract

An edge-weighting of a graph is called vertex-coloring if the weighted degrees yield a proper vertex coloring of the graph. It is conjectured that for every graph without isolated edge, a vertex-coloring edge-weighting with the set {1,2,3} exists. In this note, we show that the statement is true for the weight set {1,2,3,4}.

Keywords

Cite

@article{arxiv.2202.02788,
  title  = {Vertex-coloring graphs with 4-edge-weightings},
  author = {Ralph Keusch},
  journal= {arXiv preprint arXiv:2202.02788},
  year   = {2023}
}

Comments

6 pages

R2 v1 2026-06-24T09:22:35.909Z