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Tom and Jerry (Posted on 2021-02-16) Difficulty: 4 of 5
In the Project Euler problem Tom and Jerry, it defines Tom graphs. A cat named Tom and a mouse named Jerry play a game on a graph G. Each vertex of G is a mouse hole. Jerry hides in one of the holes. Then, Tom tries to catch Jerry by picking a hole. Then, Jerry moves to an adjacent hole. Then, Tom picks another hole. They keep doing this, where Jerry moves to an adjacent hole and Tom picks a hole. A Tom graph is a graph that Tom can always catch Jerry by following a sequence of holes.

Example: This is a Tom graph.

Tom can do the sequence 2, 2 to guarantee catching Jerry.

1. Prove that all Tom graphs are cycle-free.
2. Find the smallest cycle-free graph that is not a Tom graph.

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No Subjectslim552021-05-09 20:13:30
Part 2?Jer2021-02-20 13:43:30
Some ThoughtsA family of Tom graphs, Solution for part 1.Jer2021-02-20 13:11:06
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