Kneser graphs

The Kneser graph K(n,m) is the graph on the m-subsets of an n-set, adjacent when disjoint.

The graph K(n,m) is regular of valency (n–m choose m) (which is zero if n < 2m).

The graph K(n,m) has chromatic number n–2m+2 if n > 2m–1 (and 1 otherwise).

The Odd graphs O_m are Kneser graphs K(2m+1,m).

Kneser graphs are the distance-m graphs of the Johnson graphs, see there for some more details.