Haxell, P.E.Kierstead, H.A.2020-07-062020-07-062015-12-06https://doi.org/10.1016/j.disc.2015.06.022http://hdl.handle.net/10012/16027© 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/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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/multigraphsedge coloringGoldberg's conjectureArticle