Work

On queens and tours

Year: 2025

Type: article

Abstract: Given the complete graph on n vertices, where n ≥ 3 , we define two Hamiltonian cycles as cyclic disjoint if, for each pair of vertices, the distance between them in one Hamiltonian cycle differs from the distance between them in the other Hamiltonian cycle. We investigate the number of pairwise cyclic disjoint tours that exist in K n . Specifically, we identify when pairs of cyclic disjoint tours can occur and provide a procedure to generate m − 1 2 pairwise cyclic disjoint tours, where m is the smallest prime factor of n . Finally, we demonstrate that the number m − 1 2 of pairwise cyclic disjoint tours is maximized when n is prime.

Source: Operations Research Letters

DOI: 10.1016/j.orl.2025.107283

Authors: Pieter Jacobs, Andrés López Martínez, Frits Spieksma

Institution: Eindhoven University of Technology

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,960

Funders: European Commission, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Horizon 2020, H2020 Marie Skłodowska-Curie Actions