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Edge coloring multigraphs without small dense subsets

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EdgeColoring.pdf (275.11 KB)

Date

2015-12-06

Authors

Haxell, P.E.
Kierstead, H.A.

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

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Citation

URI

https://doi.org/10.1016/j.disc.2015.06.022
 http://hdl.handle.net/10012/16027

Collections

Waterloo Research
Combinatorics and Optimization