From a Consequence of Bertrand's Postulate to Hamilton Cycles
Combinatorics
2018-04-20 v1 Number Theory
Abstract
A consequence of Bertrand's postulate, proved by L. Greenfield and S. Greenfield in 1998, assures that the set of integers can be partitioned into pairs so that the sum of each pair is a prime number for any positive integer . Cutting through it from the angle of Graph Theory, this paper provides new insights into the problem. We conjecture a stronger statement that the set of integers can be rearranged into a cycle so that the sum of any two adjacent integers is a prime number. Our main result is that this conjecture is true for infinitely many cases.
Cite
@article{arxiv.1804.07104,
title = {From a Consequence of Bertrand's Postulate to Hamilton Cycles},
author = {Hong-Bin Chen and Hung-Lin Fu and Jun-Yi Guo},
journal= {arXiv preprint arXiv:1804.07104},
year = {2018}
}