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If any edge from a given spanning tree T0 is contained in some minimum spanning tree T*, does this imply that T0 is also a minimum spanning tree ?

Right now, I'm trying to draw on paper some graphs to prove that it doesn't. Please correct me if it does, or help me find an example if it doesn't.

Thanks in advance.

P.S. smb please add MST or spanning-trees tag.

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Any two spanning trees have the same number of edges, so if all edges in one spanning tree are also edges in the other one, then the two are in fact the same! – Mariano Suárez-Alvarez Nov 28 '10 at 1:25
a edge from T0 may be in T*1 and all the other edges, let;s say, in T*2.. both T*1 and T*2 are MST.. does this imply that T0 is also MST ? – sdadffdfd Nov 28 '10 at 1:28
up vote 4 down vote accepted

Consider a triangle with edge weights $2,2,1$.

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wow, really simple.. now the graphs I was drawing seem like aliens compared to this one, thanks. – sdadffdfd Nov 28 '10 at 1:36

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