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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 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 ...
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 ...
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.
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.
NMEA 2000, abbreviated to NMEA2k or N2K and standardized as IEC 61162-3, is a plug-and-play communications standard used for connecting marine sensors and display units within ships and boats.
The SAE J2716 SENT (Single Edge Nibble Transmission) protocol [1] is a point-to-point scheme for transmitting signal values from a sensor to a vehicle controller. It is intended to allow for transmission of high resolution data with a low system cost.
A variant, so called Compact-EDGE, was developed for use in a portion of Digital AMPS network spectrum. [3] EDGE is part of ITU's 3G definition. [4] Evolved EDGE continues in release 7 of the 3GPP standard providing reduced latency and more than doubled performance e.g. to complement High-Speed Packet Access . Peak bit-rates of up to 1 Mbit/s ...