Prove of the inequalities vertex and edge coloring Prove each of the following inequaliites:
(1) $\Delta (G) \le \chi^\prime(G)$, where $\Delta (G)$ is the maximum degree and $\chi^\prime(G)$ is the chromatic index.
Can anybody help me or give some reference about these inequalities? Thanks.

Here are some hints:
(3) Take a vertex $v$ with $\Delta(G)$ neighbors, and try coloring the edges incident to $v$. How many do you need just for that vertex ?
(4) Just do what you did for (2).  Color the edges with $\chi'(G)$ colors.  The edges belonging to a particular color class cannot touch each other, so they form a matching.
