All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
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.

1---2---3
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    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Part 2?Jer2021-02-20 13:43:30
Some ThoughtsA family of Tom graphs, Solution for part 1.Jer2021-02-20 13:11:06
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information