论文标题
平面性稀疏通用图
Sparse universal graphs for planarity
论文作者
论文摘要
我们表明，对于每个整数$ n \ geq 1 $，都有一个图$ g_n $，$（1 + o（1））n $顶点和$ n^{1 + o（1）} $ edges，使每个$ n $ n $ vertex planar graph is isomorphic is isomorphic to a $ g_n $ suberphic。 The best previous bound on the number of edges was $O(n^{3/2})$, proved by Babai, Chung, Erdős, Graham, and Spencer in 1982. We then show that for every integer $n\geq 1$ there is a graph $U_n$ with $n^{1 + o(1)}$ vertices and edges that contains induced copies of every $n$-vertex planar图。这大大减少了与Dujmović，Gavoille和Mitek的作者最近建造中的边缘数量。
We show that for every integer $n\geq 1$ there exists a graph $G_n$ with $(1+o(1))n$ vertices and $n^{1 + o(1)}$ 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, Chung, Erdős, Graham, and Spencer in 1982. We then show that for every integer $n\geq 1$ there is a graph $U_n$ with $n^{1 + o(1)}$ vertices and edges that contains induced copies of every $n$-vertex planar graph. This significantly reduces the number of edges in a recent construction of the authors with Dujmović, Gavoille, and Micek.
