algorithm - Adding the lightest possible edges without affecting the graph's minimum spanning tree? -


we have graph g , wish add edges between every vertex pair, light possible without affecting minimum spanning tree. given minimum spanning tree , pair of vertices, how 1 compute weight of lightest edge can added between them without affecting mst?

thought adding edge heavier every other edge 2 vertices have work appears erroneous in trials i've conducted.

the number of edges of spanning tree determined number of vertices. hence, if add edge mst, need remove in order spanning tree. however, cannot remove edge. obviously, removing edge not on path between 2 vertices disconnects graph. therefore, can remove edge on path. if want find minimum spanning tree, remove heaviest edge, of course.

this new spanning tree heavier original 1 iff new edge's weight greater heaviest edge weight on old path. therefore, new edge must heavier edge in order keep original mst.


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