Intersection Density of the Kneser Graph K(n,3)


A set of permutations $\mathcal{F} \subset Sym(V)$ is said to be intersecting if any two of its elements agree on some element of $V$. The intersection density, $\rho(G)$, of a finite transitive permutation group $G \leq Syn(V)$, is the maximum ratio $\frac{|\mathcal{F}| |V|}{|G|}$ where $\mathcal{F}$ runs through all intersecting sets of $G$. If the intersection density of a group is equal to 1, we say that a group has the Erdos-Ko-Rado property. The intersection density for many groups has been considered, mostly considering which groups have the Erdos-Ko-Rado property. In this talk I will consider the intersection density of a vertex-transitive graph which is defined to be the maximum value of $\rho(G)$ where is a transitive subgroup of the automorphism group of $X$. I will focus on the intersection density of the Kneser graph $K(n,3)$, for $n\geq 7$.