) Eulerian and Hamiltonian cycles. Consider the graphs defined by the following four sets of edges:...

) Eulerian and Hamiltonian cycles. Consider the graphs defined by the following four sets of edges:

a) 0-1 0-2 0-3 1-3 1-4 2-5 2-9 3-6 4-7 4-8 5-8 5-9 6-7 6-9 7-8

b) 0-1 0-2 0-3 1-3 0-3 2-5 5-6 3-6 4-7 4-8 5-8 5-9 6-7 6-9 8-8

c) 0-1 1-2 1-3 0-3 0-4 2-5 2-9 3-6 4-7 4-8 5-8 5-9 6-7 6-9 7-8

d) 4-1 7-9 6-2 7-3 5-0 0-2 0-8 1-6 3-9 6-3 2-8 1-5 9-8 4-5 4-7

1) Which of these graphs have Euler cycles (cycles that visit each edge exactly once)?

2) Which of them have Hamilton cycles (cycles that visit each vertex exactly once)?

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venereology answered 6 months ago

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