Hamiltonian cycles in some family of cubic $3$-connected plane graphs

Jan Florek

Hamiltonian cycles in some family of cubic $3$-connected plane graphs

Combinatorics 2016-08-11 v1

Authors: Jan Florek

Abstract

Barnette conjectured that all cubic $3$ -connected plane graphs with maximum face size at most $6$ are hamiltonian. We provide a method of construction of a hamiltonian cycle (in dual terms) in an arbitrary cubic, $3$ -connected plane graph possessing such a face $g$ that every face incident with $g$ has at most $5$ edges and every other face has at most $6$ edges.

Keywords

hamiltonian cycles barnette conjecture cubic graphs 3-connected plane graphs face size dual graphs graph construction

Cite

@article{arxiv.1608.03105,
  title  = {Hamiltonian cycles in some family of cubic $3$-connected plane graphs},
  author = {Jan Florek},
  journal= {arXiv preprint arXiv:1608.03105},
  year   = {2016}
}

Comments

29 pages, 28 figures

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