A note on list arboricity
An analogue of the result by \textit{F. Galvin} [J. Comb. Theory, Ser. B 63, No. 1, 153-158 (1995; Zbl 0826.05026)] is proved for edge colorings of graphs. The result by Galvin asserts that for a bipartite graph the chromatic index and the list chromatic index are equal. In this note it is shown that if the edges of a graph \(G\) can be colored by \(k\) colors such that no circuit is monochromatic then for any assignment \(E\) of \(k\) colors \(E(e)\) to each edge \(e\) of \(G\) there is a coloring of the edges choosing colors from \(E(e)\) such that no circuit is monochromatic. The result is proved in a more general form for matroids which specializes to the above statement in case \(M\) is the graphical matroid of the graph \(G\).
scientific article; zbMATH DE number 1154566