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0 Dipartite Graphs An undirected graph is bipartite if its vertices can be partitioned into two disjoint sets L,R such that each edge connects a vertex in L to a vertex in R (so there does not exist an edge that connects two vertices in L or two vertices in R ). (a) Suppose that a graph G is bipartite, with L and R being a bipartite partition of the vertices. Prove that vLdeg(v)=vRdeg(v). (b) Suppose that a graph G is bipartite, with L and R being a bipartite partition of the vertices. Let s and t denote the average degree of vertices in L and R respectively. Prove that s/t=R/L. (c) Prove that a graph is bipartite if and only if it can be 2-colored. (A graph can be 2-colored if every vertex can be assigned one of two colors such that no two adjacent vertices have the same color)