@MISC{Schulman99randomizedalgorithms, author = {Leonard Schulman}, title = {Randomized Algorithms}, year = {1999} }

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Abstract

(uv); without loss of generality assume that (uv) 2 S. This defines the cut ((S \Gamma (uv)) [ fug [ fvg; S) 2 G.) ffl The values of these cuts are equal. (Any edges of the form (xy) which cross the cut (S; S) where x; y = 2 fu; vg remain in the corresponding cut of G. Those edges of the form ((uv)y), by definition, have weight equal to the sum of at least one of the edges (uy) and/or (vy) which cross the corresponding cut of G.) ffl Contractions commute. It immediately follows that the value of the min-cut of G=(uv) is at least as great as the value of the min-cut of G. 1 We now pr