On Chromatic Number of General Kneser Graphs

Abstract

For integers $0 < i < k < n$, the general Kneser graph $K(n; k; i)$, is a graph whose vertices are subsets of size $k$ of the set ${1, 2, ..., n:}$ and two vertices $F$ and $F'$ are connected if and only if their intersection has less than i elements. In this paper we study the chromatic number of this graph. Some new bounds and properties for this chromatic number is derived.