Chromatic number of a particular graph

Assume I have a parametrized graph. The parameters are two integers $x$ and $y<x$. Let $S(x)=\{1, \ldots, x\}$. The vertices of the graph are all the subsets of $S(x)$ of size $y$. Two vertices share an edge if their intersection is empty. I need to find the chromatic number of this graph. Is this problem NP-hard ?

Thank you in advance for your help.

• – Andreas Björklund Dec 6 '11 at 19:15
• @AndreasBjörklund actualy I don't think you needed to shift this to a comment: your answer is exactly what the OP needs. – Suresh Venkat Dec 6 '11 at 19:27
• Andreas pointed out the wikipedia page, and it says the chromatic number is x-2y+2. – Yoshio Okamoto Dec 6 '11 at 22:03
• @AndreasBjörklund maybe you should undelete the answer now :) – Suresh Venkat Dec 7 '11 at 3:55
• Sorry for misunderstanding your question, I should ask you before editing... Despite this, I am still curious about the chromatic index of Kneser graphs. – Hsien-Chih Chang 張顯之 Dec 7 '11 at 4:37