A Generalization of the Erdös-Ko-Rado Theorem

Abstract

In this note, we investigate some properties of local Kneser graphs defined in [8]. In this regard, as a generalization of the Erd$\ddot{\mathrm{o}}$s-Ko-Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we present an upper bound for their chromatic number.