Abstract
Given a weighted graph, letW 1,W 2,W 3,... denote the increasing sequence of all possible distinct spanning tree weights. Settling a conjecture due to Kano, we prove that every spanning tree of weightW 1 is at mostk−1 edge swaps away from some spanning tree of weightW k . Three other conjectures posed by Kano are proven for two special classes of graphs. Finally, we consider the algorithmic complexity of generating a spanning tree of weightW k .
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This work was supported in part by a grant from the AT&T foundation and NSF grant DCR-8351757.
Primarily supported by a 1967 Science and Engineering Scholarship from the Natural Sciences and Engineering Research Council of Canada.