a. Is there an Eulerian train for the graph K₄ ? Why or why not ? If the answer is "No", give a reason. If you do not give a reason, you will not received any credit. No reason, No credit if the answer is "No".

b. Is there a Hamiltonian cycle in K₄ ? Why or why not ? If the answer is "No", give a reason. If you do not give a reason, you will not received any credit.

c. Let G be a connected graph. Let H be the graph obtained from G by removing a vertex v and any edge that is incident with v. If H is disconnected can G be Hamiltonian? Why or why not ? If the answer is "No", give a reason. If you do not give a reason, you will not received any credit.

d. Can an augmenting path have even length ? Why or why not? You must give a reason for your answer to receive credit.

e. The cycle C₂₄ is a bipartite graph. Does it have a perfect matching? Why or why not? You must give a reason for your answer to receive credit.