This will be a report of a recent joint work with Soheil Azarpendar. For integers n, k, r where n>kr-1 The Kneser hypergraph KG^r(n,k) was defined by Lovasz, Alon and Frankl as the r-uniform hypergraph with all k-subsets of {1,...,n} as vertices and its hyperedges are all r-subsets {A_1,...,A_r} of vertices that are pairwise disjoint. It was proved by them using topological methods that its chromatic number is the ceiling of (n-r(k-1))/(r-1).

Ziegler conjectured that if we take the induced sub hypergraph whose vertices are all r-stable (i.e subsets that for any two distinct elements i and j in them r-1< |i-j|

IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria www.ist.ac.at © IST 2020