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Spanning trees: Given a connected undirected graphG= (V,E), 
aspanning treeis asubgraphT= (V,E′) that is a tree (connected graph with no cycles). 
Note thatTcontainsall vertices ofGand, becauseTis a tree, it has exactly|V|−1 edges.
SupposeGhas nonnegative edge weightsw(e).  
Theweightof a spanning treeT= (V,E′)is the total weight of all its edges, i.e.∑e∈E′w(e).  
Aminimum spanning treeis a spanningtree of smallest weight.  As you may know, 
there are greedy algorithms such as Prim’s andKruskal’s that find minimum spanning trees very efficiently.
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