Hamiltonicity in Prime Sum Graphs

Hong Bin Chen, Hung Lin Fu, Jun Yi Guo

研究成果: 雜誌貢獻期刊論文同行評審

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
頁(從 - 到)209-219
頁數11
期刊Graphs and Combinatorics
37
發行號1
DOIs
出版狀態接受/付印 - 2020

ASJC Scopus subject areas

  • 理論電腦科學
  • 離散數學和組合

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