Maximum andk-th maximal spanning trees of a weighted graph

Abstract

LetA be a maximum spanning tree andP be an arbitrary spanning tree of a connected weighted graphG. Then we prove that there exists a bijectionψ fromA/P intoP/A such that for any edgeaA/P, (P/ψ(a)) ∪a is a spanning tree ofG whose weight is greater than or equal to that ofP. We apply this theorem to some problems concerning spanning trees of a weighted graph.

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Kano, M. Maximum andk-th maximal spanning trees of a weighted graph. Combinatorica 7, 205–214 (1987). https://doi.org/10.1007/BF02579450

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  • 05 C 05