Acta Mathematicae Applicatae Sinica

, Volume 4, Issue 3, pp 266–268 | Cite as

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

  • Liu Zhenhong 


Let ℱ (G) be the collection of all spanning trees of a connected and weighted graphG, andF1,F2, ...,F m the partition of ℱ (G) such thatF n the set ofi-th maximal spanning trees ofG. Kano[1] conjectured that for anyAF1 and every integerk, 1≤km, there existsTF k such that |T/A|≤k−1. This paper gives the conjecture a very simple proof, and related results.


Span Tree Related Result Simple Proof Math Application Maximal Span 


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  1. [1]
    Kano, Mikio, Maximum andk-th Maximal Spanning Tree of a Weighted Graph.Combinatorica,7: 2 (1987), 205.Google Scholar
  2. [2]
    Kawamoto, T., Kajitoni, Y. and Shinoda, S., On the Second Maximal Tree of a Weighted Graph,Trans. IECE of Japan,61-A (1978), 988–995.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1988

Authors and Affiliations

  • Liu Zhenhong 
    • 1
  1. 1.Institute of Systems Science, Academia SinicaChina

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