On the diameter of Kneser graphs

Abstract

Let n and k be positive integers. The Kneser graph $K_n^{2n+k}$ is the graph with vertex set $[2n+k{]}^n$ and where two n-subsets $A,B\in [2n+k{]}^n$ are joined by an edge if $A\cap B=\varnothing$. In this note, we show that the diameter of the Kneser graph $K_n^{2n+k}$ is equal to $\lceil (n-1)/k\rceil +1$.