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k-edge-connected graph - Wikipedia


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 ...

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 ...

Lecture 13 1 Global Min-Cut and Edge-Connectivity - Stanford CS ...


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 ... - NCBI


Fig 3 depicts the k-edge-connected components of the graph in Fig 2 for k ∈ {1, 2 , 3} (note that for h > 3, the collection of ...

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 ...



edge-connected if the graph remains connected even after deleting fewer edges than k ... A k-edge-connected graph G is said to be minimally k-connected if G.

A synthesis for exactly 3-edge-connected graphs - arXiv.org


May 7, 2009 ... We define a multigraph G to be exactly k-edge-connected if there are exactly k ... G is a k-edge-connected graph, but not necessarily exactly ...

2-Connected Graphs Definition 1 A graph is connected if for any two ...


A separating set or vertex cut of a connected graph G is a set. S ⊂ V (G) such ... A connected graph G is called k-edge-connected if every discon- necting edge ...

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


Abstract. 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 ...

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Chapter 5 Connectivity


Similarly, adding a new vertex of degree k to a k-edge-connected graph yields a ... 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 ... Lemma 2 Every minimally k-edge-connected graph G = (V,E) has a vertex of degree k. Proof: Let S ⊆ V be minimal such that d(S) := |δ(S)| = k.

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


Fig 3 depicts the k-edge-connected components of the graph in Fig 2 for k ∈ {1, 2 , 3} (note that for h > 3, the collection of ...