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Topic: Is "connected graphs" -> P(trees), G|->{spanning trees of G} one-to-one?
Replies: 6   Last Post: Mar 15, 2004 11:00 AM

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Dan Luecking

Posts: 45
Registered: 12/13/04
Re: Is "connected graphs" -> P(trees), G|->{spanning trees of G} one-to-one?
Posted: Mar 5, 2004 6:39 PM
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On Thu, 04 Mar 2004 11:56:49 -0600, Dan Luecking <>

>On Tue, 2 Mar 2004 20:20:59 +0100, "sasha"
>< (AT)> wrote:

>>Hello everyone!
>>For a given natural number m, is the map
>>connected graphs with m edges -> power set of trees,
>>G |-> {spanning trees of G}

>Yes, for simple graphs. No, if loops or parallel edges are allowed:
>a graph with one loop and one simple edge has the same spanning tree
>as a graph with two edges connecting the same 2 vertices.

Oops. I suppose the latter has two spanning trees corresponding to
the two parallel edges. Replace this example with: G1 has a loop at x
and an edge from x to y. While G2 has an edge from x to y and a loop
at y.

One should always be clear what "different" and "same" mean. I clearly


Dan Luecking Department of Mathematical Sciences
University of Arkansas Fayetteville, Arkansas 72701
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