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

Carsten Thomassen; Carol T. Zamfirescu

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

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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
Journal	Australasian Journal of Combinatorics
Volume	81
Issue number	2
Pages (from-to)	334–338
ISSN	1034-4942
Publication status	Published - 2021

Keywords

Hamiltonian cycle
Regular graph

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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.",

keywords = "Hamiltonian cycle, Regular graph",

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

year = "2021",

language = "English",

volume = "81",

pages = "334–338",

journal = "Australasian Journal of Combinatorics",

issn = "1034-4942",

publisher = "Centre for Discrete Mathematics & Computing",

number = "2",

}

TY - JOUR

T1 - 4-regular 4-connected Hamiltonian graphs with a bounded number of Hamiltonian cycles

AU - Thomassen, Carsten

AU - Zamfirescu, Carol T.

PY - 2021

Y1 - 2021

N2 - 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.

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.

KW - Hamiltonian cycle

KW - Regular graph

M3 - Journal article

VL - 81

SP - 334

EP - 338

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

IS - 2

ER -

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

Abstract

Keywords

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