A generalization of the Erdös–Ko–Rado theorem

AbstractIn this note, we investigate some properties of local Kneser graphs defined in [János Körner, Concetta Pilotto, Gábor Simonyi, Local chromatic number and sperner capacity, J. Combin. Theory Ser. B 95 (1) (2005) 101–117]. In this regard, as a generalization of the Erdös–Ko–Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we provide an upper bound for their chromatic number

Locally restricted colorings of graphs

Let G be a simple graph and f a function from the vertices of G to the set of positive integers. An (f, n)-coloring of G is an assignment of n colors to the vertices of G such that each vertex x is adjacent to less than f(x) vertices with the same color as x. The minimum n such that an (f, n)-coloring of G exists is defined to be the fchromatic number of G. In this paper, we address a study of this kind of locally restricted coloring.