Graph Theory: 08-b Basic Problem Set (part 2/2)

Here we provide solutions to a basic problem set in Graph Theory. This part 2 of 2 answers the following:
3) For k = 0,1 and 2, characterize the k-regular graphs.
4) Prove that in a bipartite graph with partite sets X and Y, the sum of the degrees of the vertices in X is equal to the sum of the degrees of the vertices in Y.
5) Prove OR find a counterexample to the following statement: "If u,v,w are vertices of a graph and there is an even length path from u to v and an even length path from v to w, then there is an even length path from u to w."
--An introduction to Graph Theory by Dr. Sarada Herke.
Links to the related videos:
• Graph Theory: 08-a Bas... - Graph Theory: 08-a Basic Problem Set (part 1/2)
• Graph Theory: 05. Conn... - Graph Theory: 05. Connected and Regular Graphs
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