Hamilton decompositions of one-ended Cayley graphs

Joshua Erde*, Florian Lehner*, Max Pitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove that any one-ended, locally finite Cayley graph G(Γ,S), where Γ is an abelian group and S is a finite generating set of non-torsion elements, admits a decomposition into edge-disjoint Hamiltonian (i.e. spanning) double-rays. In particular, the n-dimensional grid Z n admits a decomposition into n edge-disjoint Hamiltonian double-rays for all n∈N.

Original languageEnglish
Pages (from-to)171-191
Number of pages21
JournalJournal of Combinatorial Theory, Series B
Publication statusPublished - Jan 2020
Externally publishedYes


  • Alspach conjecture
  • Cayley graph
  • Double ray
  • Hamilton decomposition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Fields of Expertise

  • Information, Communication & Computing


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