4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles

Carsten Thomassen; Carol T Zamfirescu

doi:10.48550/arXiv.2104.06347

4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles

Carsten Thomassen, Carol T Zamfirescu

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

3 Citations (Scopus)

Abstract

We prove that there exists an infinite family of 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles. We do not know whether there exists such a family of 5-regular 5-connected Hamiltonian graphs.

Original language	English
Pages (from-to)	334-338
Number of pages	5
Journal	Australasian Journal of Combinatorics
Volume	81
Issue number	2
DOIs	https://doi.org/10.48550/arXiv.2104.06347
Publication status	Published - Apr 2021
Externally published	Yes

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© The author(s). Released under the CC BY-ND 4.0 International License.

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Cite this

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title = "4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles",

abstract = "We prove that there exists an infinite family of 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles. We do not know whether there exists such a family of 5-regular 5-connected Hamiltonian graphs.",

author = "Carsten Thomassen and Zamfirescu, {Carol T}",

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AU - Zamfirescu, Carol T

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AB - We prove that there exists an infinite family of 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles. We do not know whether there exists such a family of 5-regular 5-connected Hamiltonian graphs.

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DO - 10.48550/arXiv.2104.06347

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JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

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4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles

Abstract

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