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Nonhamiltonian 3-Connected Cubic Planar Graphs

Authors:

R. E. L. Aldred,

S. Bau,

D. A. Holton,

Brendan D. McKayAuthors Info & Claims

SIAM Journal on Discrete Mathematics, Volume 13, Issue 1

Pages 25 - 32

https://doi.org/10.1137/S0895480198348665

Published: 01 January 2000 Publication History

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Abstract

We establish that every cyclically 4-connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp, and we present all nonhamiltonian examples of order 42. In addition we list all nonhamiltonian cyclically 5-connected cubic planar graphs of order at most 52 and all nonhamiltonian 3-connected cubic planar graphs of girth 5 on at most 46 vertices. The fact that all 3-connected cubic planar graphs on at most 176 vertices and with face size at most 6 are hamiltonian is also verified.

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Wigal MYu X(2025)On Tutte Cycles Containing Three Prescribed EdgesGraphs and Combinatorics10.1007/s00373-025-02886-w41:1Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s00373-025-02886-w
Ghorbani MSonghori M(2016)On the automorphism group of polyhedral graphsApplied Mathematics and Computation10.1016/j.amc.2016.01.066282:C(237-243)Online publication date: 5-May-2016
https://dl.acm.org/doi/10.1016/j.amc.2016.01.066
Schauerte BZamfirescu C(2015)Small k-pyramids and the complexity of determining kJournal of Discrete Algorithms10.1016/j.jda.2014.11.00330:C(13-20)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.jda.2014.11.003
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Index Terms

Nonhamiltonian 3-Connected Cubic Planar Graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics Volume 13, Issue 1

Jan. 2000

144 pages

ISSN:0895-4801

Editor:
David B. Shmoys
Cornell Univ., Ithaca, NY

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2000

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Wigal MYu X(2025)On Tutte Cycles Containing Three Prescribed EdgesGraphs and Combinatorics10.1007/s00373-025-02886-w41:1Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s00373-025-02886-w
Ghorbani MSonghori M(2016)On the automorphism group of polyhedral graphsApplied Mathematics and Computation10.1016/j.amc.2016.01.066282:C(237-243)Online publication date: 5-May-2016
https://dl.acm.org/doi/10.1016/j.amc.2016.01.066
Schauerte BZamfirescu C(2015)Small k-pyramids and the complexity of determining kJournal of Discrete Algorithms10.1016/j.jda.2014.11.00330:C(13-20)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.jda.2014.11.003
Raspaud AWang W(2008)On the vertex-arboricity of planar graphsEuropean Journal of Combinatorics10.1016/j.ejc.2007.11.02229:4(1064-1075)Online publication date: 1-May-2008
https://dl.acm.org/doi/10.1016/j.ejc.2007.11.022
Kutnar KMarušič D(2008)On cyclic edge-connectivity of fullerenesDiscrete Applied Mathematics10.1016/j.dam.2007.08.046156:10(1661-1669)Online publication date: 1-May-2008
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