On the intersection density of the Kneser Graph K(n,3)

2022/05/10 by Meagher, Karen, Razafimahatratra, Andriaherimanana Sarobidy · 1 citation
#05C35 #05C69 #20B05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.05118

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 density ρ(G) is the maximum ratio (|F||V|)/(|G|) where F runs through all intersecting sets of G. The intersection density ρ(X) of a vertex-transitive graph X = (V,E) is equal to max \ ρ(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.

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