Advanced search
1 file | 297.01 KB

On hypohamiltonian snarks and a theorem of Fiorini

Jan Goedgebeur (UGent) and Carol Zamfirescu (UGent)
(2018) ARS MATHEMATICA CONTEMPORANEA. 14(2). p.227-249
Author
Organization
Project
HPC-UGent: the central High Performance Computing infrastructure of Ghent University
Abstract
In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini's theorem from 1983 on hypohamiltonian snarks. However, their version of this theorem contains an unattainable condition for certain cases. We discuss and extend the results of Fiorini and Cavicchioli et al. and present a version of this theorem which is more general in several ways. Using Fiorini's erroneous result, Steffen had shown that hypohamiltonian snarks exist for some orders n >= 10 and each even n >= 92. We rectify Steffen's proof by providing a correct demonstration of a technical lemma on flower snarks, which might be of separate interest. We then strengthen Steffen's theorem to the strongest possible form by determining all orders for which hypohamiltonian snarks exist. This also strengthens a result of Macajova and Skoviera. Finally, we verify a conjecture of Steffen on hypohamiltonian snarks up to 36 vertices.
Keywords
Hypohamiltonian, snark, irreducible snark, dot product, CUBIC GRAPHS, COVERS, ORDER

Downloads

  • 1176-6443-1-PB.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 297.01 KB

Citation

Please use this url to cite or link to this publication:

Chicago
Goedgebeur, Jan, and Carol Zamfirescu. 2018. “On Hypohamiltonian Snarks and a Theorem of Fiorini.” Ars Mathematica Contemporanea 14 (2): 227–249.
APA
Goedgebeur, J., & Zamfirescu, C. (2018). On hypohamiltonian snarks and a theorem of Fiorini. ARS MATHEMATICA CONTEMPORANEA, 14(2), 227–249.
Vancouver
1.
Goedgebeur J, Zamfirescu C. On hypohamiltonian snarks and a theorem of Fiorini. ARS MATHEMATICA CONTEMPORANEA. 2018;14(2):227–49.
MLA
Goedgebeur, Jan, and Carol Zamfirescu. “On Hypohamiltonian Snarks and a Theorem of Fiorini.” ARS MATHEMATICA CONTEMPORANEA 14.2 (2018): 227–249. Print.
@article{8545503,
  abstract     = {In 2003, Cavicchioli et al. corrected an omission in the statement and proof of Fiorini's theorem from 1983 on hypohamiltonian snarks. However, their version of this theorem contains an unattainable condition for certain cases. We discuss and extend the results of Fiorini and Cavicchioli et al. and present a version of this theorem which is more general in several ways. Using Fiorini's erroneous result, Steffen had shown that hypohamiltonian snarks exist for some orders n >= 10 and each even n >= 92. We rectify Steffen's proof by providing a correct demonstration of a technical lemma on flower snarks, which might be of separate interest. We then strengthen Steffen's theorem to the strongest possible form by determining all orders for which hypohamiltonian snarks exist. This also strengthens a result of Macajova and Skoviera. Finally, we verify a conjecture of Steffen on hypohamiltonian snarks up to 36 vertices.},
  author       = {Goedgebeur, Jan and Zamfirescu, Carol},
  issn         = {1855-3966},
  journal      = {ARS MATHEMATICA CONTEMPORANEA},
  keywords     = {Hypohamiltonian,snark,irreducible snark,dot product,CUBIC GRAPHS,COVERS,ORDER},
  language     = {eng},
  number       = {2},
  pages        = {227--249},
  title        = {On hypohamiltonian snarks and a theorem of Fiorini},
  url          = {https://amc-journal.eu/index.php/amc/article/view/1176},
  volume       = {14},
  year         = {2018},
}

Web of Science
Times cited: