CyclesAndColorings

You are given a connected undirected graph G = (V,E). We define a simple cycle to be $Good$, if it consists of an odd number of edges, and if on deleting all those edges, the graph still remains connected. Note that we do not delete any vertices. A $4 - Coloring$ of the graph is an assignment of colors to the vertices of the graph and which satisfies these properties: - Every vertex should be as