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2. Cut (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Cut_(graph_theory)

   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 ...

3. Vertex separator - Wikipedia

   en.wikipedia.org/wiki/Vertex_separator

   More precisely, there is always exactly one or exactly two vertices, which amount to such a separator, depending on whether the tree is centered or bicentered. [ 2 ] As opposed to these examples, not all vertex separators are balanced , but that property is most useful for applications in computer science, such as the planar separator theorem .

4. Minimum cut - Wikipedia

   en.wikipedia.org/wiki/Minimum_cut

   The dotted line in red represents a cut with three crossing edges. The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] 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.

5. Menger's theorem - Wikipedia

   en.wikipedia.org/wiki/Menger's_theorem

   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.

6. Connectivity (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Connectivity_(graph_theory)

   More generally, an edge cut of G is a set of edges whose removal renders the graph disconnected. The edge-connectivity λ(G) is the size of a smallest edge cut, and the local edge-connectivity λ(u, v) of two vertices u, v is the size of a smallest edge cut disconnecting u from v. Again, local edge-connectivity is symmetric.

7. Karger's algorithm - Wikipedia

   en.wikipedia.org/wiki/Karger's_algorithm

   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