Minimal spanning trees
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- by James H. Schmerl PDF
- Proc. Amer. Math. Soc. 132 (2004), 333-340 Request permission
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.References
- Peter G. Clote and Jeffry L. Hirst, Reverse mathematics of some topics from algorithmic graph theory, Fund. Math. 157 (1998), no. 1, 1–13. MR 1619288, DOI 10.4064/fm-157-1-1-13
- Stephen G. Simpson, Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1999. MR 1723993, DOI 10.1007/978-3-642-59971-2
Additional Information
- James H. Schmerl
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06269-3009
- MR Author ID: 156275
- ORCID: 0000-0003-0545-8339
- Email: schmerl@math.uconn.edu
- 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.
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 333-340
- MSC (2000): Primary 05C05, 03B30, 03D80
- DOI: https://doi.org/10.1090/S0002-9939-03-07182-X
- MathSciNet review: 2022353