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arXiv · 2306.04565

Prime sum graphs and the induced trees they contain

Ernie Croot·Patrick Jin
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Abstract

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.

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Ernie Croot, Patrick Jin. 2023-06-07. Prime sum graphs and the induced trees they contain. https://arxiv.org/abs/2306.04565

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