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.
Chromatic number of a particular graph
cc.complexity theory;np hardness;graph colouring
See http://en.wikipedia.org/wiki/Kneser_graph