Hamilton decompositions of one-ended Cayley graphs

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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 admits a decomposition into n edge-disjoint Hamiltonian double-rays for all n.
Original languageEnglish
JournalJournal of Combinatorial Theory / B
Volume140
Publication statusPublished - 2020

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Hamiltonians
Cayley Graph
Half line
Disjoint
Decomposition
Decompose
Generating Set
Finite Graph
Abelian group
n-dimensional
Finite Set
Grid

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Hamilton decompositions of one-ended Cayley graphs. / Erde, Joshua; Pitz, Max; Lehner, Florian.

In: Journal of Combinatorial Theory / B, Vol. 140, 2020.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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 admits a decomposition into n edge-disjoint Hamiltonian double-rays for all n.

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