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Hamiltonicity in graphs defined by primes and primitive elements
Abstract
A prime circle of order 2n is a circular ordering of 1,…,2n such that the sum of every two adjacent terms is prime. We prove that a prime circle exists for every sufficiently large n. The proof is based on a perfect matching and robust expansion. We also study Hamilton cycles in graphs and digraphs defined by primitive sums and differences over finite fields. In particular, the primitive-sum graph on Fq is Hamiltonian for every prime power q>18 888 871, and for the graph on a full prime field Fp, the bound improves to p>61.
Related
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BibTeX
@misc{she2026hamiltonicity,
title = {{Hamiltonicity in graphs defined by primes and primitive elements}},
author = {Yue-Feng She},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19114},
eprint = {2609.19114},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19114},
}
RIS
TY - UNPB
TI - Hamiltonicity in graphs defined by primes and primitive elements
AU - Yue-Feng She
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19114
UR - https://arxiv.org/abs/2609.19114
AB - A prime circle of order 2n is a circular ordering of 1,…,2n such that the sum of every two adjacent terms is prime. We prove that a prime circle exists for every sufficiently large n. The proof is based on a perfect matching and robust expansion. We also study Hamilton cycles in graphs and digraphs defined by primitive sums and differences over finite fields. In particular, the primitive-sum graph on F_q is Hamiltonian for every prime power q>18 888 871, and for the graph on a full prime field F_p, the bound improves to p>61.
ER -