Problem 11.32. Prove the following facts of any graph G = (V, E) with n vertices. (2) There are at least two vertices with the same degree (degree twins). b) One can partition V into two sets so that every vertex in a set has at least half its neighbors in the other set. every vertex has degree at least 6 > 2, there is a cycle of length at least + 1. (d) If every vertex has degree at least n/2, the graph is connected. (e) If the degrees of non-adjacent vertices sum to at least n 1, the graph is connected