Prime sum graphs and the induced trees they contain

Ernie Croot; Patrick Jin

Prime sum graphs and the induced trees they contain

Number Theory 2023-06-08 v1 Combinatorics

Authors: Ernie Croot , Patrick Jin

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.

Keywords

spanning trees graph theory trees

Cite

@article{arxiv.2306.04565,
  title  = {Prime sum graphs and the induced trees they contain},
  author = {Ernie Croot and Patrick Jin},
  journal= {arXiv preprint arXiv:2306.04565},
  year   = {2023}
}

Comments

This was part of an undergrad research project that Patrick did with me last year

Related papers

View all related →