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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 ...

k-Edge-Connected Graph -- from Wolfram MathWorld

mathworld.wolfram.com/k-Edge-ConnectedGraph.html

-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 ...

Chapter 5 Connectivity

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

k-connected. Similarly, a graph is k-edge connected if it has at least two vertices and no set of k −1 edges is a separator. The edge-connectivity of G, denoted by ...

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 ...

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 ...

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

theory.stanford.edu/~trevisan/cs261/lecture13.pdf

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 ...

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

www.sciencedirect.com/science/article/pii/S0166218X02004651

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.

Paths in k-edge-connected graphs - ScienceDirect.com

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 ...

On k-minimally n-edge-connected graphs - ScienceDirect.com

www.sciencedirect.com/science/article/pii/0012365X7890198X

A graph is k-minimal with respect to some parameter if the removal of any j edges j<k reduces the value of that parameter by j. For k = 1 this concept is ...

The maximal size of graphs with at most k edge-disjoint paths ...

www.sciencedirect.com/science/article/pii/0012365X9090161A

A graph G is said to be minimally k-edge-connected if .1(G) = k and R(G - e) = k - 1 for each edge a of G. An edge cut of a graph G is a subset of E(G) of the form ...

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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 ...

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

journals.plos.org

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

k-edge-connected graph problem - Mathematics Stack Exchange

math.stackexchange.com

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 ...