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k-edge-connected graph


In graph theory, a connected graph is k-edge-connected if it remains connected whenever fewer than k edges are removed. The edge-connectivity of a graph is ...

k-Edge-Connected Graph -- from Wolfram MathWorld


-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a ...

Lecture 13 1 Global Min-Cut and Edge-Connectivity


Feb 17, 2011 ... 1 Global Min-Cut and Edge-Connectivity. Definition 1 (Edge connectivity) We say that an undirected graph is k-edge-connected if one needs to ...

A Simple Algorithm for Finding All k-Edge-Connected Components


Sep 14, 2015 ... The problem of finding k -edge-connected components is a fundamental problem in computer science. Given a graph G = ( V , E ), the problem ...

Graph Theory - Personal.kent.edu


The edge-connectivity λ(G) of a connected graph G is the smallest number of edges whose removal disconnects G. When λ(G) ≥ k, the graph G is said to be ...

Generating k-Vertex Connected Spanning Subgraphs and k-Edge ...

rutcor.rutgers.edu/~kborys/k connected.pdf

Abstract. We show that k-vertex connected spanning subgraphs of a given graph ... Input: A positive integer k and a k-edge connected graph G. Output: The list of ...

On minimally k-edge-connected graphs and shortest ... - ScienceDirect


A graph G=(V,E) is called minimally (k,T)-edge-connected with respect to some T ⊆V if there exist k-edge-disjoint paths between every pair u,v∈T but this pro.

A Simple Algorithm for Finding All k-Edge-Connected ... - NCBI


Sep 14, 2015 ... The problem of finding k-edge-connected components is a fundamental problem in computer science. Given a graph G = (V, E), the problem is ...

Graph Theory


Jul 24, 2015 ... k − 1 ≥ δ and k ≥ δ + 1, and our path has at least δ edges. Let i (1 ≤ i ... Proof. Every connected graph with at least two vertices has an edge.

Connectivity Edge-connectivity Characterization of 2-connected ...


in a k-connected graph is ⌈kn/2⌉. Proof: min ≥ ⌈kn/2⌉, since k ≤ κ(G) ≤ δ(G) min ≤ ⌈kn/2⌉; Example: Harary graphs Hk,n. 1. Edge-connectivity. An edge cut  ...

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Chapter 5 Connectivity


Similarly, a graph is k-edge connected if it has at least two vertices and no set of k −1 ... vertex x adjacent to at least k vertices of G, then G is k-edge-connected.

Lecture 19 1 k-edge-connectivity


Nov 12, 2009 ... parallel edges. 1. 2 k. Then any 2k-connected multigraph G = (V,E) can ... Lemma 2 Every minimally k-edge-connected graph G = (V,E) has a ...

k-edge-connected graph problem - Mathematics Stack Exchange


Dec 27, 2012 ... Prove or disprove: If G is a k-edge-connected graph with nonempty disjoint subsets S 1 and S 2 of V ( G ) , then there exist k edge-disjoint paths ...