Work

Arc-disjoint hamiltonian paths in Cartesian products of directed cycles

Year: 2024

Type: article

Abstract: We show that if C1 and C2 are directed cycles (of length at least two), then the Cartesian product C1 □ C2 has two arc-disjoint hamiltonian paths. (This answers a question asked by J. A. Gallian in 1985.) The same conclusion also holds for the Cartesian product of any four or more directed cycles (of length at least two), but some cases remain open for the Cartesian product of three directed cycles. We also discuss the existence of arc-disjoint hamiltonian paths in 2-generated Cayley digraphs on (finite or infinite) abelian groups.

Source: Ars Mathematica Contemporanea

DOI: 10.26493/1855-3974.3047.c2d

Authors: Iren Darijani, Babak Miraftab, Dave Witte Morris

Institutions: Memorial University of Newfoundland, Carleton University, University of Lethbridge

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4401646860

FWCI: 0.196

Cites: 23

Cited by: 1

Related to: 10