Journal
DISCRETE MATHEMATICS
Volume 343, Issue 2, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.disc.2019.111654
Keywords
Signed graph; Edge coloring; Vizing
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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. (C) 2019 Elsevier B.V. All rights reserved.
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