Clique number of Xor products of Kneser graphs

In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in “A general 2-part Erdős-Ko-Rado theorem” by Gyula O.H. Katona, who proposed our problem as well. In the graph theoretic form we examine the clique number of the Xor product of two isomorphic KG(N,k) Kneser graphs. Denote this number with f(k,N). We give lower and upper bounds on f(k,N), and we solve the problem up to a constant deviation depending only on k, and find the exact value for f(2,N) if N is large enough. Also we compute that f(k,k2) is asymptotically equivalent to k2.