We show that for every integer $n\geq 1$ there exists a graph $G_n$ with $n^{1 + o(1)}$ edges such that every $n$-vertex planar graph is isomorphic to a subgraph of $G_n$. The best previous bound on the number of edges was $O(n^{3/2})$, proved by Babai, Erd\H{o}s, Chung, Graham, and Spencer in 1982.

翻译：我们显示,对于每整数美元1美元,就有一个以美元1美元+o(1)美元为边端的G$_n美元图,这样,每一美元反向平面图就等于以美元为底线。 1982年Babai、Erd\H{o}s、Chung、Graham和Spencer证明,以前对边缘数的最佳约束是O美元(n ⁇ 3/2})美元。