10. (4 Points) Consider the graphs defined by the following four sets of edges: a) 0-2...

 

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10. (4 Points) Consider the graphs defined by the following four sets of edges: a) 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 b) 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 c) 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 Which of these graphs have Euler cycles (cycles that visit each edge exactly once)? Which of them have Hamilton cycles (cycles that visit each vertex exactly once except the starting and ending vertex)? 10. (4 Points) Consider the graphs defined by the following four sets of edges: a) 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 b) 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 c) 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 Which of these graphs have Euler cycles (cycles that visit each edge exactly once)? Which of them have Hamilton cycles (cycles that visit each vertex exactly once except the starting and ending vertex)?