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In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. [1] Any cut determines a cut-set, the set of edges that have one endpoint ...
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. Variations of the minimum cut problem consider weighted graphs, directed graphs, terminals, and partitioning the vertices into more than two sets.
Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut in the theory of flow networks. Thanks to the max-flow min-cut theorem , determining the minimum cut over a graph representing a flow network is equivalent to computing the maximum flow over the ...
The vertex-connectivity statement of Menger's theorem is as follows: . Let G be a finite undirected graph and x and y two nonadjacent vertices. Then the size of the minimum vertex cut for x and y (the minimum number of vertices, distinct from x and y, whose removal disconnects x and y) is equal to the maximum number of pairwise internally disjoint paths from x to y.
A graph and two of its cuts. The dotted line in red is a cut with three crossing edges. The dashed line in green is a min-cut of this graph, crossing only two edges. In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David Karger and first ...
A min-cut of a weighted graph having min-cut weight 4 [1] In graph theory, the Stoer–Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights. It was proposed by Mechthild Stoer and Frank Wagner in 1995.
A man’s sandwich-cutting ingenuity has reignited a debate on what is truly the best way to cut a sandwich. On Saturday, April 27, X user Ryan Duff was first inspired to go against the whole ...
An edge is said to span the partition if it has endpoints in both subsets. Thus, the removal of a cut-set from a connected graph disconnects it. cut point See articulation point. cut space The cut space of a graph is a GF(2)-vector space having the cut-set s of the graph as its elements and symmetric difference of sets as its vector addition ...
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