English

On the algorithmic complexity of finding hamiltonian cycles in special classes of planar cubic graphs

Combinatorics 2018-06-19 v1

Abstract

It is a well-known fact that hamiltonicity in planar cubic graphs is an NP-complete problem. This implies that the existence of an A-trail in plane eulerian graphs is also an NP-complete problem even if restricted to planar 3-connected eulerian graphs. In this paper we deal with hamiltonicity in planar cubic graphs G having a facial 2-factor Q via (quasi) spanning trees of faces in G/Q and study the algorithmic complexity of finding such (quasi) spanning trees of faces. We show, in particular, that if Barnette's Conjecture is false, then hamiltonicity in 3-connected planar cubic bipartite graphs is an NP-complete problem.

Keywords

Cite

@article{arxiv.1806.06713,
  title  = {On the algorithmic complexity of finding hamiltonian cycles in special classes of planar cubic graphs},
  author = {Behrooz Bagheri Gh. and Tomas Feder and Herbert Fleischner and Carlos Subi},
  journal= {arXiv preprint arXiv:1806.06713},
  year   = {2018}
}

Comments

17 pages, 0 figures. arXiv admin note: text overlap with arXiv:1806.05483