A conjecture on the prevalence of cubic bridge graphs

Jerzy Filar; Michael Haythorpe; Giang Nguyen

doi:10.7151/dmgt.1485

A conjecture on the prevalence of cubic bridge graphs

Jerzy Filar
, Michael Haythorpe
, Giang Nguyen

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

5 Citations (Scopus)

Abstract

Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.

Original language	English
Pages (from-to)	175-179
Number of pages	5
Journal	Discussiones Mathematicae. Graph Theory
Volume	30
Issue number	1
DOIs	https://doi.org/10.7151/dmgt.1485
Publication status	Published - 2010

Keywords

Cubic bridge graph
Hamiltonian graph
Non-Hamiltonian graph

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10.7151/dmgt.1485

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title = "A conjecture on the prevalence of cubic bridge graphs",

abstract = "Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.",

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AU - Filar, Jerzy

AU - Haythorpe, Michael

AU - Nguyen, Giang

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N2 - Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.

AB - Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.

KW - Cubic bridge graph

KW - Hamiltonian graph

KW - Non-Hamiltonian graph

UR - http://www.discuss.wmie.uz.zgora.pl/gt/30_1/gt30-779.htm

UR - https://www.scopus.com/pages/publications/77956550118

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DO - 10.7151/dmgt.1485

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JO - Discussiones Mathematicae. Graph Theory

JF - Discussiones Mathematicae. Graph Theory

IS - 1

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A conjecture on the prevalence of cubic bridge graphs

Abstract

Keywords

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