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A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
In graph theory, a vertex subset is a vertex separator (or vertex cut, separating set) for nonadjacent vertices a and b if the removal of S from the graph separates a and b into distinct connected components.
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.
cut-set A cut is a partition of the vertices of a graph into two subsets, or the set (also known as a cut-set) of edges that span such a partition, if that set is non-empty. 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 ...
A vertex cut or separating set of a connected graph G is a set of vertices whose removal renders G disconnected. The vertex connectivity κ(G) (where G is not a complete graph) is the size of a smallest vertex cut. A graph is called k-vertex-connected or k-connected if its vertex connectivity is k or greater.
A cut (,) in an undirected graph = (,) is a partition of the vertices into two non-empty, disjoint sets =.The cutset of a cut consists of the edges {:,} between the two parts. . The size (or weight) of a cut in an unweighted graph is the cardinality of the cutset, i.e., the number of edges between the two parts
An s-t cut C = (S, T) is a partition of V such that s ∈ S and t ∈ T. That is, an s-t cut is a division of the vertices of the network into two parts, with the source in one part and the sink in the other. The cut-set of a cut C is the set of edges that connect the source part of the cut to the sink part:
A variation of the planar separator theorem involves edge separators, small sets of edges forming a cut between two subsets and of the vertices of the graph. The two sets and must each have size at most a constant fraction of the number of vertices of the graph (conventionally, both sets have size at most /), and each vertex of the graph ...