Algorithms & Complexity

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Let G = (V, E) be an undirected graph such that each vertex has degree ≥ k, i.e., using the notation from the textbook for degree,∀v ∈ V, nv ≥ k. (a) Prove that G includes a path of length k. (b) Give me an algorithm that will find a path of length k for any undirected graph where all nodes have degree ≥ k. (k will be a parameter of the algorithm.) Provide the time-complexity of your algorithm (with sufficient explanation); it should be possible to do this in O(k 2) time.

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