On Edge Coloring of Multigraphs

Let $Δ(G)$ and $χ'(G)$ be the maximum degree and chromatic index of a graph $G$, respectively. Gupta\,(1967), Goldberg\,(1973), Andersen\,(1977), and Seymour\,(1979) made the following conjecture: Every multigraph $G$ satisfies $χ'(G) \le \max\{ Δ(G) + 1, Γ(G) \}$, where $Γ(G) = \max_{H \subseteq