Find the number of undirected graphs on vertices such that, whenever there is a path joining the vertices , then there is a complete graph on .

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- July 7th 2009, 01:54 PMBruno J.Find the number of graphs such that...
Find the number of undirected graphs on vertices such that, whenever there is a path joining the vertices , then there is a complete graph on .

- July 8th 2009, 12:51 AMSwlabr
I can't think of any hints that wouldn't be completely and utterly cryptic, so I'll just sort of give you the logical leap bit, and is hopefully only a wee bit cryptic...presuming, of course, you didn't quite get the leap bit...

Basically, what you want to do find out how many ways there are of partitioning and n-element set.

I'm sure you can solve the problem from there.