Towards k-vertex connected component discovery from large networks

Enumerating k-Vertex Connected Components in Large Graphs

Cohesive subgraph detection is an important graph problem that is widely applied in many application domains, such as social community detection, network visualization, and network topology analysis. Most of existing cohesive subgraph metrics can guarantee good structural properties but may cause the free-rider effect. Here, by free-rider effect, we mean that some irrelevant subgraphs are combi...

Generating Minimal k-Vertex Connected Spanning Subgraphs

We show that minimal k-vertex connected spanning subgraphs of a given graph can be generated in incremental polynomial time for any fixed k.

Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

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

We show that k-vertex connected spanning subgraphs of a given graph can be generated in incremental polynomial time for any fixed k. We also show that generating k-edge connected spanning subgraphs, where k is part of the input, can be done in incremental polynomial time. These results are based on properties of minimally k-connected graphs which might be of independent interest.

Outer-k-connected component domination in graphs

A subset S of the vertices of a graph G is an outer-connected dominating set, if S is a dominating set of G and G − S is connected. The outer-connected domination number of G, denoted by γ̃c(G), is the minimum cardinality of an OCDS of G. In this paper we generalize the outer-connected domination in graphs. Many of the known results and bounds of outer-connected domination number are immediate c...