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A solution to one of Kano's conjectures concerningk-th maximal spanning trees

A solution to one of Kano's conjectures concerningk-th maximal spanning trees Let ℱ (G) be the collection of all spanning trees of a connected and weighted graphG, andF 1,F 2, ...,F m the partition of ℱ (G) such thatF n the set ofi-th maximal spanning trees ofG. Kano[1] conjectured that for anyA ∈F 1 and every integerk, 1≤k≤m, there existsT ∈F k such that |T/A|≤k−1. This paper gives the conjecture a very simple proof, and related results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A solution to one of Kano's conjectures concerningk-th maximal spanning trees

Liu, Zhenhong
Acta Mathematicae Applicatae Sinica , Volume 4 (3) – Jul 13, 2005
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 1988 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006223
Publisher site
See Article on Publisher Site

Abstract

Let ℱ (G) be the collection of all spanning trees of a connected and weighted graphG, andF 1,F 2, ...,F m the partition of ℱ (G) such thatF n the set ofi-th maximal spanning trees ofG. Kano[1] conjectured that for anyA ∈F 1 and every integerk, 1≤k≤m, there existsT ∈F k such that |T/A|≤k−1. This paper gives the conjecture a very simple proof, and related results.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 13, 2005

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