The p-restricted edge-connectivity of Kneser graphs

Abstract

Given a connected graph G and an integer 1¿=¿p¿=¿¿|V(G)|/2¿, a p-restricted edge-cut of G is any set of edges S¿¿¿E(G), if any, such that is not connected and each component of has at least p vertices; and the p-restricted edge-connectivity of G, denoted ¿p(G), is the minimum cardinality of such a p-restricted edge-cut. When p-restricted edge-cuts exist, G is said to be super-¿p if the deletion from G of any p-restricted edge-cut S of cardinality ¿p(G) yields a graph that has at least one component with exactly p vertices. In this work, we prove that Kneser graphs K(n, k) are ¿p-connected for a wide range of values of p. Moreover, we obtain the values of ¿p(G) for all possible p and all n¿=¿5 when . Also, we discuss in which cases ¿p(G) attains its maximum possible value, and determine for which values of p graph is super-¿p.