On the intersection density of the Kneser Graph $K(n,3)$
| Autor: | Meagher, Karen, Razafimahatratra, Andriaherimanana Sarobidy |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A set $\mathcal{F} \subset \operatorname{Sym}(V)$ is \textsl{intersecting} if any two of its elements agree on some element of $V$. Given a finite transitive permutation group $G\leq \operatorname{Sym}(V)$, the \textsl{intersection density} $\rho(G)$ is the maximum ratio $\frac{|\mathcal{F}||V|}{|G|}$ where $\mathcal{F}$ runs through all intersecting sets of $G$. The \textsl{intersection density} $\rho(X)$ of a vertex-transitive graph $X = (V,E)$ is equal to $\max \left\{ \rho(G) : G \leq \operatorname{Aut}(X) \mbox{ is transitive} \right\}$. In this paper, we study the intersection density of the Kneser graph $K(n,3)$, for $n\geq 7$. The intersection density of $K(n,3)$ is determined whenever its automorphism group contains $\operatorname{PSL}_{2}(q)$ or $\operatorname{PGL}_{2}(q)$, with some exceptional cases depending on the congruence of $q$. Comment: 15 pages |
| Databáze: | arXiv |
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