On the intersection density of the Kneser graph [formula omitted

Abstract

A set F⊂Sym(V) is intersecting if any two of its elements agree on some element of V. Given a finite transitive permutation group G≤Sym(V), the intersection densityρ(G) is the maximum ratio |F||V||G| where F runs through all intersecting sets of G. The intersection densityρ(X) of a vertex-transitive graph X=(V,E) is equal to maxρ(G):G≤Aut(X),G transitive. In this paper, we study the intersection density of the Kneser graph K(n,3), for n≥7. The intersection density of K(n,3) is determined whenever its automorphism group contains PSL2(q), with some exceptional cases depending on the congruence of q. We also briefly consider the intersection density of K(n,2) for values of n where PSL2(q) is a subgroup of its automorphism group.