Please Answer the second part of the question. AKA the Alternating path, redux. Thanks in advance.

Alternating paths. Let G -(V, E) be a directed graph. Suppose every node v has a color c[v], which is either black or white. Let k be a positive integer. A path in G is called k-alternating if it changes color at least k times. Note that such a path need not be simple (that is, it may contain repeated nodes). For example, consider the following graph: The path A CB+D+E is a 3-alternating path. The path A 5-alternating path C BD -EC -B is a