English

Circumference of essentially 4-connected planar triangulations

Combinatorics 2021-01-28 v2

Abstract

A 33-connected graph GG is essentially 44-connected if, for any 33-cut SV(G)S\subseteq V(G) of GG, at most one component of GSG-S contains at least two vertices. We prove that every essentially 44-connected maximal planar graph GG on nn vertices contains a cycle of length at least 23(n+4)\frac{2}{3}(n+4); moreover, this bound is sharp.

Keywords

Cite

@article{arxiv.2101.03802,
  title  = {Circumference of essentially 4-connected planar triangulations},
  author = {Igor Fabrici and Jochen Harant and Samuel Mohr and Jens M. Schmidt},
  journal= {arXiv preprint arXiv:2101.03802},
  year   = {2021}
}