An extension of Vizing's adjacency lemma of edge chromatic critical graphs (Q1304811)

Vizing's adjacency lemma (VAL) describes an important property of edge-chromatic critical graphs, namely in an edge-chromatic critical simple graph \(G\) of the maximum degree \(\Delta \), if \(xy\) is an edge, \(x\) is adjacent with at least \(\Delta -\text{deg}(y)+1\) vertices \((\neq y)\) of degree \(\Delta \). One of the generalizations of this result to multigraphs is due to \textit{L. D. Andersen} [Math. Scand. 40, No.~2, 161-175 (1977; Zbl 0373.05035)]. In this paper an extension of Andersen's result is proposed.