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    Minimum Spanning Tree

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    Given a graph G and a minimum spanning tree T, suppose that we decrease the weight of one of the edges in T. Show that T is still a minimum spanning tree for G. More formally, let T be a minimum spanning tree for G with edge weights given by weight function w. Choose one edge (x, y) is a subset of T and a positive number k, and define the weight function w' by

    w'(u,v) = w(u,v) if (u, v) =/ (x,y)
    w(x,y) - k if (u,v) = (x,y)

    Show that T is a minimum spanning tree for G with edge weights given by w'.

    © BrainMass Inc. brainmass.com November 30, 2021, 12:57 am ad1c9bdddf
    https://brainmass.com/computer-science/trees/minimum-spanning-tree-73417

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