We show that any connected Cayley graph $\Gamma$ on an Abelian group of order $2n$ and degree $\tilde{\Omega}(\log n)$ has at most $2^{n+1}(1 + o(1))$ independent sets. This bound is tight up to to the $o(1)$ term when $\Gamma$ is bipartite. Our proof is based on Sapozhenko's graph container method and uses the Pl\"{u}nnecke-Rusza-Petridis inequality from additive combinatorics.

翻译：我们显示任何连接的Cayley 图形$\ Gamma$ 在Abelian 一组订单上 $n$ $ 和 $\ tilde\ Omega} (\log n) $\ log n$ $ 最多有 2\ n+1} (1 + o(1)) 美元独立套件。 当$\ Gamma$是两部分时, 这个套件紧凑到 $ (1) 的 $ (1) 期限 。 我们的证据是基于 Sapozhenko 的图形容器方法, 并使用 Pl\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ n\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\