G. Boruzanli Ekinci, J.B. Gauci
The super-connectivity of Kneser graphs
Discussiones Mathematicae Graph Theory
Received 10.10.2016, Revised 18.03.2017, Accepted 18.03.2017, doi: 10.7151/dmgt.2051

A vertex cut of a connected graph G is a set of vertices whose deletion disconnects G. A connected graph G is super-connected if the deletion of every minimum vertex cut of G isolates a vertex. The super-connectivity is the size of the smallest vertex cut of G such that each resultant component does not have an isolated vertex. The Kneser graph KG(n,k) is the graph whose vertices are the k-subsets of {1,2,...,n} and two vertices are adjacent if the k-subsets are disjoint. We use Baranyai's Theorem on the decompositions of complete hypergraphs to show that the Kneser graph KG(n,2) are super-connected when n≥ 5 and that their super-connectivity is {n\choose 2}-6 when n≥ 6.
connectivity, super-connectivity, Kneser graphs