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Topic: Menger's theorem question
Replies: 5   Last Post: Jan 20, 2011 11:58 AM

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Posts: 1,089
Registered: 12/6/04
Re: Menger's theorem question
Posted: Jan 20, 2011 11:58 AM
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On Jan 17, 6:28 pm, Robert Israel
<isr...@math.MyUniversitysInitials.ca> wrote:

> Surely it depends on the polyhedron?  E.g. for an octahedron there
> are 4 pairwise vertex-independent paths between non-adjacent
> vertices.

4 paths for adjacent vertices too.

Indeed the number of pairwise vertex-independent paths for any pair of
non-identical vertices from any Platonic polyhedron is equal to the
number of edges meeting at each vertex (so 3 for a tetrahedron, cube
or dodecahedron, 4 for an octahedron and 5 for an icosahedron).

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