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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal spanning trees


Author: James H. Schmerl
Journal: Proc. Amer. Math. Soc. 132 (2004), 333-340
MSC (2000): Primary 05C05, 03B30, 03D80
Published electronically: September 12, 2003
MathSciNet review: 2022353
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Abstract: The main result is that a recursive weighted graph having a minimal spanning tree has a minimal spanning tree that is $\Delta^0_2$. This leads to a proof of the failure of a conjecture of Clote and Hirst (1998) concerning Reverse Mathematics and minimal spanning trees.


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Additional Information

James H. Schmerl
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06269-3009
Email: schmerl@math.uconn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07182-X
PII: S 0002-9939(03)07182-X
Keywords: Spanning trees, reverse mathematics
Received by editor(s): August 21, 2002
Received by editor(s) in revised form: October 3, 2002
Published electronically: September 12, 2003
Additional Notes: Thanks to the referee and Jeff Hirst for their help in identifying a serious flaw in the original version of this paper
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2003 American Mathematical Society