Solution
= Solution
The <Vizing theorem> states that for every finite simple <graph> of maximum <vertex degree> $\Delta$, its <edge chromatic number> satisfies $\boxed{\Delta\le\chi'(G)\le\Delta+1}$. The lower bound follows because all edges incident to a maximum-degree vertex need different colors. The simplicity hypothesis matters: unrestricted <multigraphs> need not satisfy this upper bound.