# decrease weight of edges in graph [duplicate]

Suppose given complete undirected weighted graph $$G=(V,E)$$ with $$n$$ vertices, also we have Minimum spanning tree $$T$$ that obtained from $$G$$. if we decrease the weight of $$n$$ arbitrary edges, how we can find MST of $$G$$ without computing MST of $$G$$?

My idea is as follow:

1. create a graph $$T'$$ with $$n$$ vertices that contains those edges that decreased.

2. Compute MST $$T''$$ from $$T\cup T'$$.

now suppose MST of $$G$$ after decrease edges weights be $$T'''$$, but I can't prove that $$T'''=T''$$.