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