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Subject: "Theorem of Wilson."     Previous Topic | Next Topic
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sfwc
Member since Jun-19-03
Jun-28-05, 08:23 AM (EST)
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"Theorem of Wilson."
 
   The theorem of Wilson generalising the solution to the fifteen puzzle appears to have a problem. In particular, consider any nonbipartite graph G with a node N such that removal of N disconnects G. Then evidently puz(G) is not connected. For example, consider the graph A which looks like a letter A. puz(A) has 12 connected components.

It appears that if you include the condition that removal of any node leaves the graph connected then the theorem is saved.

Thankyou

sfwc
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alexbadmin
Charter Member
1567 posts
Jun-28-05, 10:06 AM (EST)
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1. "RE: Theorem of Wilson."
In response to message #0
 
   You are right. For the theorem to hold, the base graph should be nonseparable. Being connected is not enough.

Many thanks,
Alex


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