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2. 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.

3. k-edge-connected graph - Wikipedia

   en.wikipedia.org/wiki/K-edge-connected_graph

   The edge connectivity of is the maximum value k such that G is k-edge-connected. The smallest set X whose removal disconnects G is a minimum cut in G . The edge connectivity version of Menger's theorem provides an alternative and equivalent characterization, in terms of edge-disjoint paths in the graph.

4. Connectivity (graph theory) - Wikipedia

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

   The connectivity and edge-connectivity of G can then be computed as the minimum values of κ(u, v) and λ(u, v), respectively. In computational complexity theory , SL is the class of problems log-space reducible to the problem of determining whether two vertices in a graph are connected, which was proved to be equal to L by Omer Reingold in ...

5. k-vertex-connected graph - Wikipedia

   en.wikipedia.org/wiki/K-vertex-connected_graph

   The vertex-connectivity of an input graph G can be computed in polynomial time in the following way [4] consider all possible pairs (,) of nonadjacent nodes to disconnect, using Menger's theorem to justify that the minimal-size separator for (,) is the number of pairwise vertex-independent paths between them, encode the input by doubling each vertex as an edge to reduce to a computation of the ...

6. Max-flow min-cut theorem - Wikipedia

   en.wikipedia.org/wiki/Max-flow_min-cut_theorem

   In the undirected edge-disjoint paths problem, we are given an undirected graph G = (V, E) and two vertices s and t, and we have to find the maximum number of edge-disjoint s-t paths in G. Menger's theorem states that the maximum number of edge-disjoint s-t paths in an undirected graph is equal to the minimum number of edges in an s-t cut-set.

7. Biconnected graph - Wikipedia

   en.wikipedia.org/wiki/Biconnected_graph

   A biconnected undirected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex (and its incident edges).. A biconnected directed graph is one such that for any two vertices v and w there are two directed paths from v to w which have no vertices in common other than v and w.

8. Troubleshoot a broadband internet connection - AOL Help

   help.aol.com/articles/troubleshooting-a...

   Check the physical connection - A loose cable or cord can often be the cause of a connection problem. Make sure everything is securely connected to the wall and device. 3. Reboot your modem/router - Sometimes the old "turn it off and on again" approach actually does work! Just wait about five minutes before turning it back on to make sure ...

9. Strong connectivity augmentation - Wikipedia

   en.wikipedia.org/wiki/Strong_connectivity...

   Strong connectivity augmentation is a computational problem in the mathematical study of graph algorithms, in which the input is a directed graph and the goal of the problem is to add a small number of edges, or a set of edges with small total weight, so that the added edges make the graph into a strongly connected graph.