Question: 2b. Let G=(V, E) be an undirected graph with n=|V| vertices and m=|E| edges: Prove that G contains a cycle if and only if a

2b. Let G=(V, E) be an undirected graph with n=|V| vertices and m=|E| edges:

Prove that G contains a cycle if and only if a BFS traversal of G contains a cross edge.

Your solution can use the following basic facts from graph theory: 1. There exists a unique path between any two vertices of a tree. 2. Adding any edge to a tree creates a unique cycle.

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