Enumerating k-Arc-Connected Orientations

Parity Constrained k-Edge-Connected Orientations

On Frank's conjecture on k-connected orientations

We disprove a conjecture of Frank [4] stating that each weakly 2k-connected graph has a k-vertex-connected orientation. For k ≥ 3, we also prove that the problem of deciding whether a graph has a k-vertex-connected orientation is NP-complete.

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...

Enumerating Cyclic Orientations of a Graph

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the prob...

Enumerating orientations of the free spikes

We show that there are exactly 2Dk inequivalent orientations of the rank-k free spike (k ≥ 4) where Dk is the k th Dedekind number. Our proof of this result is constructive and employs the monotone boolean functions.