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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. Menger sponge - Wikipedia

    en.wikipedia.org/wiki/Menger_sponge

    Menger showed, in the 1926 construction, that the sponge is a universal curve, in that every curve is homeomorphic to a subset of the Menger sponge, where a curve means any compact metric space of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in ...

  4. 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 ...

  5. 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.

  6. List of 7400-series integrated circuits - Wikipedia

    en.wikipedia.org/wiki/List_of_7400-series...

    4-digit up/down counter, decoder and LCD driver, output latch 40 MM74C945: 74x946 1 4.5-digit counter, decoder and LCD driver, leading zero blanking 40 MM74C946: 74x947 1 4-digit up/down counter, decoder and LCD driver, leading zero blanking 40 MM74C947: 74x948 1 8-bit ADC with 16-channel analog multiplexer analog three-state 40 MM74C948: 74x949 1

  7. Max-flow min-cut theorem - Wikipedia

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

    A maximal flow in a network. Each edge is labeled with f/c, where f is the flow over the edge and c is the edge's capacity. The flow value is 5. There are several minimal s-t cuts with capacity 5; one is S={s,p} and T={o, q, r, t}. The figure on the right shows a flow in a network.