# Hamiltonicity in Prime Sum Graphs

Hong Bin Chen*, Hung Lin Fu, Jun Yi Guo

*此作品的通信作者

## 摘要

For any positive integer n, we define the prime sum graph Gn= (V, E) of order n with the vertex set V= { 1 , 2 , ⋯ , n} and E={ij:i+jisprime}. Filz in 1982 posed a conjecture that G2n is Hamiltonian for any n≥ 2 , i.e., the set of integers { 1 , 2 , ⋯ , 2 n} can be represented as a cyclic rearrangement so that the sum of any two adjacent integers is a prime number. With a fundamental result in graph theory and a recent breakthrough on the twin prime conjecture, we prove that Filz’s conjecture is true for infinitely many cases.

原文 英語 209-219 11 Graphs and Combinatorics 37 1 https://doi.org/10.1007/s00373-020-02241-1 已發佈 - 2021 1月

• 理論電腦科學
• 離散數學和組合