1. a b c d e f g h j i k Graph G is shown. Which of the following is a trail but not a path? 1). acdefhg 2). hfdcbdfe 3). ghfdcbde 4). acdegik 5). None of them 6). All of them

2. a b c d e f g h j i k Graph G is shown. What is the length of the shortest c-g path? 1 2 3 4 5 6 7 8

3. What is the first line of this proof? 1). Let v 1 v 2 …v n be a u-v walk. 2). Let v 1 v 2 …v n be a u-v path. 3). Assume that if P is a u-v walk, then P contains a u-v path.

4. a b c d e f g h j i k Graph G is shown. How many different cycles are there starting at e? 1234 567 8

5. What is the first line of this proof? 1). Assume G is bipartite. 2). Assume G has no odd cycles. 3). Let C be an odd cycle.

6. What is the next line of this proof if we are doing a proof by contradiction? 1). Assume C is an even cycle. 2). Assume G has no odd cycles. 3). Let C be an odd cycle. 4). Let C be any cycle. 5). Assume that there are no even cycles.

7. What is the first line of this proof? 1). Assume G is bipartite. 2). Assume G has no odd cycles. 3). Let C be an odd cycle.