标题： 素数和图及其包含的诱导树 显示英文标题

标题： Prime sum graphs and the induced trees they contain

摘要： 在本文中，我们证明了顶点数为$n$的素数和图——即顶点集为$\{1,2,...,n\}$的图，当$i+j$为素数时，$ij$是边——包含最多$\exp( c \log n / \log\log n)$个顶点的所有树作为诱导子图。我们还证明了一些相关图的结果，并以一些未解决的问题结束。 显示英文摘要

摘要： In this paper we show that prime sum graphs on $n$ vertices -- which are graphs on vertex set $\{1,2,...,n\}$ where $ij$ is an edge when $i+j$ is prime -- contain all trees with at most $\exp( c \log n / \log\log n)$ vertices as induced subgraphs. We also prove some results for related graphs, and end with some unsolved problems.