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k-edge-connected graph

en.wikipedia.org/wiki/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 ...

Chapter 5 Connectivity

www-sop.inria.fr/members/Frederic.Havet/Cours/connectivity.pdf

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.

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

journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264

It is well-known that the set of k-edge-connected components (k ≥ 1) is a partition of V. Moreover, each k-edge-connected ...

Paths in k-edge-connected graphs - ScienceDirect

www.sciencedirect.com/science/article/pii/0095895688900779

We prove (i) if G is a 2k-edge-connected graph (k≥2), s, t are vertices, and f1, f2, g are edges with fi ≠ g (i=1, 2), then there exists a cycle C passing through f1 ...

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

www.ncbi.nlm.nih.gov/pmc/articles/PMC4569431/

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 ...

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

www.cs.rpi.edu/~goldberg/15-GT/07-connectivity.pdf

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 ...

k-edge-connected graph problem - Mathematics Stack Exchange

math.stackexchange.com/questions/265812/k-edge-connected-graph-problem

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 ...

k-edge-connected graph- proof - Mathematics Stack Exchange

math.stackexchange.com/questions/167881/k-edge-connected-graph-proof

Jul 7, 2012 ... Call a graph k-edge connected iff for every set X of fewer than k edges, G | X is connected. Prove that every 2-edge connected graph has a ...

A connected graph $G$ is $k$-edge-connected $\iff$ each block of ...

math.stackexchange.com/questions/1751046/a-connected-graph-g-is-k-edge-connected-iff-each-block-of-g-is-k-edge

Apr 20, 2016 ... A graph G is k -edge-connected if every disconnecting set of edges (i.e. edge set D such that G ′ = ( V , E ∖ D ) is disconnected) has at least k ...

Graph Theory - Personal.kent.edu

www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/connectivity.htm

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 ...

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k-Edge-Connected Graph -- from Wolfram MathWorld

mathworld.wolfram.com

-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 19 1 k-edge-connectivity

math.mit.edu

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 ...

CS261 Lecture 13: Edge Connectivity | in theory

lucatrevisan.wordpress.com

Feb 21, 2011 ... Definition 1 (Edge connectivity) We say that an undirected graph is {k} -edge- connected if one needs to remove at least {k} edges in order to ...