On the diameter of generalized Kneser graphs

Let r, k be positive integers, s(<r), a nonnegative integer, and n=2r-s+k. The set of r-subsets of n]={1,2,…,n} is denoted by n]^r. The generalized Kneser graph K(n,r,s) is the graph whose vertex-set is n]^r where two r-subsets A and B are joined by an edge if |A∩B|?s. This note determines the diameter of generalized Kneser graphs. More precisely, the diameter of K(n,r,s) is equal to , which generalizes a result of Valencia-Pabon and Vera On the diameter of Kneser graphs, Discrete Math. 305 (2005) 383-385].