Edge coloring multigraphs without small dense subsets
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Date
2015-12-06
Authors
Haxell, P.E.
Kierstead, H.A.
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
One consequence of a long-standing conjecture of Goldberg and Seymour about the chromatic index of multigraphs would be the following statement. Suppose $G$ is a multigraph with maximum degree $\Delta$, such that no vertex subset $S$ of odd size at most $\Delta$ induces more than $(\Delta+1)(|S|-1)/2$ edges. Then $G$ has an edge coloring with $\Delta+1$ colors. Here we prove a weakened version of this statement.
Description
© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
multigraphs, edge coloring, Goldberg's conjecture