2018/04/19 by Hongbin Chen, Chen, Hong-Bin, Hung‐Lin Fu +3
Computer Science · Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1804.07104
openalex publication_date 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A consequence of Bertrand's postulate, proved by L. Greenfield and S. Greenfield in 1998, assures that the set of integers \1,2,⋯, 2n\ can be partitioned into pairs so that the sum of each pair is a prime number for any positive integer n. 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 \1,2,⋯, 2n\ 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.