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Dec 1, 2013 at 9:48 answer added Aaron Meyerowitz timeline score: 2
Dec 1, 2013 at 2:03 answer added hbm timeline score: 0
Dec 1, 2013 at 2:00 comment added Richard Stanley It's even false for regular connected graphs of degree three; there is a counterexample with ten vertices.
Dec 1, 2013 at 1:39 comment added bof I guess you mean connected graph of minimum degree $3$; non-connected graphs don't have spanning trees. If every vertex of the spanning tree has odd degree ($1$ or $3$), the number of vertices must be even by the "handshake" lemma. For a counterexample to your question, take any connected graph of minimum degree $3$ with an odd number of vertices, say $K_5-e$. By the way, your question is off topic for this site, next time try math.stackexchange.com.
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Dec 1, 2013 at 1:23 history edited Rick CC BY-SA 3.0
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Dec 1, 2013 at 1:05 history asked Rick CC BY-SA 3.0