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.
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