English

Edge Coloring Signed Graphs

Combinatorics 2018-12-05 v2

Abstract

We define a method for edge coloring signed graphs and what it means for such a coloring to be proper. Our method has many desirable properties: it specializes to the usual notion of edge coloring when the signed graph is all-negative, it has a natural definition in terms of vertex coloring of a line graph, and the minimum number of colors required for a proper coloring of a signed simple graph is bounded above by {\Delta} + 1 in parallel with Vizing's Theorem. In fact, Vizing's Theorem is a special case of the more difficult theorem concerning signed graphs.

Keywords

Cite

@article{arxiv.1807.11465,
  title  = {Edge Coloring Signed Graphs},
  author = {Richard Behr},
  journal= {arXiv preprint arXiv:1807.11465},
  year   = {2018}
}

Comments

31 pages, 13 figures