Course Solutions Uncategorized (Solved) : 15pts Prove Digraph G V E Directed Cycle Dfs G Detects Back Edge Proof Follows Coloring Co Q30420886 . . . .

(Solved) : 15pts Prove Digraph G V E Directed Cycle Dfs G Detects Back Edge Proof Follows Coloring Co Q30420886 . . . .

 

(15pts) we prove that a digraph G=(V, E) has a directed cycle if and only if DFS(G) detects a back edge. The proof follows the coloring convention given in class. 1, If-part: Suppose G has back edge e?(1, w). The edge e is colored in--(a) when DFS(G) detects it. We have a cycle created by e and all the (b)edges under_ (c)at the time of detection. This proves the if-part. Only-if-part: Suppose G has a directed cycle C [v, vz, ., v, v1). We can without loss of generality assume that v, is the first node to be 

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