I have a simple proof.
Assume existing two different spanning trees, say Ta and Tb.
Let Ea={edges of Ta} Eb={edges of Tb}
Let e be the maximum weighted edge that belongs to either of Ea and Eb but
not both.
Assume e belongs to Ea. We remove e from Ta, and Ta becomes two disjoint
sub-trees Ta1 and Ta2.
There must exist a edge e' in Eb connecting Ta1 and Ta2 with a smaller
weight than e.
so we can connect Ta1 and Ta2 with e' to get a spanning tree of smaller
weight than Ta.
On 7/9/07, TheTravellingSalesman <[EMAIL PROTECTED]> wrote:
>
>
> Prove that there is a unique minimum spanning tree on a connected
> undirected graph when the edge weights
> are unique.
>
>
>
> ===============================================================================
>
> Makes intuitive sense but yet, I'm having a hard time trying to prove
> it. I tried induction but I'm stuck...... any suggestions?
>
>
> >
>
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