The forbidden-matching avoidance conjecture

Let $G$ be a multigraph with maximum degree $\Delta(G)$ and maximum multiplicity $\mu(G)$. A forbidden matching is a matching whose edges have been assigned arbitrary, not necessarily proper, colours from a palette. The forbidden-matching avoidance conjecture. Using the palette $\mathcal{K}=[\Delta(G)+\mu(G)]$, any forbidden matching can be avoided by a proper edge-colouring of all of $G$, meaning that the colouring disagrees with the assigned colour on every forbidden edge. This is a significant weakening of the edge-precolouring extension conjecture and is not implied by the List Colouring Conjecture; its proof was left open in the paper.