Non-Hamiltonian Cartesian products of two even dicycles

Kenta Noguchi; Carol T. Zamfirescu

doi:10.1002/jgt.23185

Non-Hamiltonian Cartesian products of two even dicycles

Kenta Noguchi
, Carol T. Zamfirescu

Tokyo University of Science
Ghent University
Babes-Bolyai University

Research output: Contribution to journal › Article › peer-review

Abstract

In this note it is proven that there exist infinitely many positive integers (Formula presented.) and (Formula presented.) such that the Cartesian product of a directed cycle of length (Formula presented.) and a directed cycle of length (Formula presented.) is non-Hamiltonian. In particular, the Cartesian product of an 880-dicycle and a 4368-dicycle is non-Hamiltonian. We also prove that there is no such graph on fewer than (Formula presented.) vertices, which is rather astonishing.

Original language	English
Pages (from-to)	368–373
Number of pages	6
Journal	Journal of Graph Theory
Volume	108
Issue number	2
DOIs	https://doi.org/10.1002/jgt.23185
Publication status	Published - Feb 2025
Externally published	Yes

Bibliographical note

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© 2024 Wiley Periodicals LLC.

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10.1002/jgt.23185

Cite this

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abstract = "In this note it is proven that there exist infinitely many positive integers (Formula presented.) and (Formula presented.) such that the Cartesian product of a directed cycle of length (Formula presented.) and a directed cycle of length (Formula presented.) is non-Hamiltonian. In particular, the Cartesian product of an 880-dicycle and a 4368-dicycle is non-Hamiltonian. We also prove that there is no such graph on fewer than (Formula presented.) vertices, which is rather astonishing.",

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AB - In this note it is proven that there exist infinitely many positive integers (Formula presented.) and (Formula presented.) such that the Cartesian product of a directed cycle of length (Formula presented.) and a directed cycle of length (Formula presented.) is non-Hamiltonian. In particular, the Cartesian product of an 880-dicycle and a 4368-dicycle is non-Hamiltonian. We also prove that there is no such graph on fewer than (Formula presented.) vertices, which is rather astonishing.

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SP - 368

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JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 2

ER -

Non-Hamiltonian Cartesian products of two even dicycles

Abstract

Bibliographical note

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