The decomposition of graphs into k-connected components

Decomposing Infinite 2-Connected Graphs into 3-Connected Components

In the 1960’s, Tutte presented a decomposition of a 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on 2-connected graphs to problems on 3-connected graphs. Motivated by a problem concerning accumulation points of infinite planar graphs, we generalize Tutte’s decomposition to include all infinite 2-connected graphs.

Efficient GPU algorithms for parallel decomposition of graphs into strongly connected and maximal end components

This article presents parallel algorithms for component decomposition of graph structures on general purpose graphics processing units (GPUs). In particular, we consider the problem of decomposing sparse graphs into strongly connected components, and decomposing graphs induced by stochastic games (such as Markov decision processes) into maximal end components. These problems are key ingredients...

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...

Decomposition of 3-connected graphs

The atomic decomposition of strongly connected graphs

We define and study a new canonical decomposition of strongly connected graphs that we call the atomic decomposition. We can construct it in linear time from the decomposition in 3-connected components of the considered graph. In a companion article, we use it to characterize, up to homeomorphism, all closed curves in the plane having a given Gauss word.