Search results
Results from the WOW.Com Content Network
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.
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 ...
A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
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.
The canonical optimization variant of the above decision problem is usually known as the Maximum-Cut Problem or Max-Cut and is defined as: Given a graph G, find a maximum cut. The optimization variant is known to be NP-Hard. The opposite problem, that of finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm.
Consider a graph G = (V, E), where V denotes the set of n vertices and E the set of edges. For a (k,v) balanced partition problem, the objective is to partition G into k components of at most size v · (n/k), while minimizing the capacity of the edges between separate components. [1]
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 ...