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  • 1 Post By gyarenas1
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July 15th, 2016, 07:00 AM   #1
Joined: Jul 2016
From: China

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Math Focus: Graph Theory
A graph theory problem about spanning tree

Given a simple connected graph G, suppose T_1 and T_2 are two different spanning trees of G and E(T_1)\E(T_2)={a_1, a_2, ..., a_s}, E(T_2)\E(T_1)={b_1, b_2, ..., b_s}. Then, there exist a permutation {p_1, p_2, ..., p_s} such that T_1-a_i+b_{p_i} (i = 1, 2,...,s) is still a spanning tree of G.

Is the above proposition true? If it is, how to prove? Thanks!
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