We show that every proper minor-closed class of graphs admits a $(1+o(1))\log_2 n$-bit adjacency labelling scheme. Equivalently, for every proper minor-closed class $\mathcal{G}$ and every positive integer $n$ there exists an $n^{1+o(1)}$-vertex graph $U$ such that every $n$-vertex graph in $\mathcal{G}$ is isomorphic to an induced subgraph of $U$. Both results are optimal up to the lower order term.

翻译：我们证明每个真闭子图类存在一个$(1+o(1))\log_2 n$比特的邻接标号方案。等价地，对于每个真闭子图类$\mathcal{G}$和每个正整数$n$，存在一个$n^{1+o(1)}$个顶点的图$U$，使得$\mathcal{G}$中每个$n$顶点图都与$U$的某个导出子图同构。这两项结果在低阶项范围内均是最优的。