A SOLUTION TO ONE OF KANO'S CONJECTURES CONCERNING k-th MAXIMAL SPANNING TREES

Let (G) be the collection of all spanning trees of a connected and weighted graph G,and F_1, F_2,…,F_m the partition of (G) such that F_i is the set of i-th maximal spanning trees of G.Kano conjectured that for any A∈F_1 and every integer k,1≤k≤m,there exists T∈F_k such that|T/A| k—l.This paper gives the conjecture a very simple proof,and related results.