Exercise 1 (6 points). Let G (V, E) be a finite graph and let a, b E V. Let n be the number of 1. Prove that if there exists a walk from a to b of length m 2 n, then there also exists a walk 2. Next, argue that if there exists a walk from a to b of length m 2n, then there are an infinite elements in V. (The length of a walk w is the number of edges in w.) from a to b of length k > m. (Hint: Use the Pigeonhole Principle.) number walks from a to b