Question: Let G be a graph. Suppose that a depth-first search traversal of G starting at an arbitrary vertex results in a depth-first search forest

Let G be a graph. Suppose that a depth-first search traversal of G starting at an arbitrary vertex results in a depth-first search forest that is a path (that is to say, each level of the tree contains only one vertex). Does this imply that G is a complete graph? Know how to perform a depth-first search traversal of a graph and how to construct a depth-first search forest, and you should do fine.

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