Minimal spanning trees
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The main result is that a recursive weighted graph having a minimal spanning tree has a minimal spanning tree that is Δ 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.
[1] Stephen G. Simpson,et al. Subsystems of second order arithmetic , 1999, Perspectives in mathematical logic.
[2] Reverse mathematics of some topics from algorithmic graph theory , 1998 .