Recall the following statement from Worksheet 11: Theorem 1. If G = (V, E) is a simple graph (no loops or multi-edges) with |V] = n > 3 vertices, and each pair of vertices a, b eV with a, b distinct and non-adjacent satisfies deg(a) + deg(6) > n, then G has a Hamilton cycle. (a) Using this fact, or otherwise, prove or disprove: Every connected undirected graph having degree sequence 2, 2, 4, 4, 6 has a Hamilton cycle. (b) The statement: Every connected undirected graph having degree sequence 2, 2, 4, 4,6 has a Hamilton cycle is A. True B. False.
