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On the spanning trees of weighted graphs

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Graph-Theoretic Concepts in Computer Science (WG 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 344))

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Abstract

Given a weighted graph, let W 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 weight W 1 is at most k — 1 edge swaps away from some spanning tree of weight W 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 weight W k.

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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Authors
  1. Ernst W. Mayr
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  2. C. Greg Plaxton
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Editor information

J. van Leeuwen

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© 1989 Springer-Verlag Berlin Heidelberg

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Mayr, E.W., Plaxton, C.G. (1989). On the spanning trees of weighted graphs. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1988. Lecture Notes in Computer Science, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50728-0_58

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  • DOI: https://doi.org/10.1007/3-540-50728-0_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50728-4

  • Online ISBN: 978-3-540-46076-3

  • eBook Packages: Springer Book Archive

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