On the spanning trees of weighted graphs

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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Additional information

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.

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Mayr, E.W., Plaxton, C.G. On the spanning trees of weighted graphs. Combinatorica 12, 433–447 (1992). https://doi.org/10.1007/BF01305236

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AMS subject classification code (1991)

  • 05 C 05
  • 05 C 85
  • 68 R 10