@article{FHMS21maximalessentially4connected,
title = {Circumference of essentially 4-connected planar triangulations},
author = {Fabrici, Igor and Harant, Jochen and Mohr, Samuel and Schmidt, Jens M},
journal = {Journal of Graph Algorithms and Applications},
year = {2021},
volume = {25},
number = {1},
pages = {121--132},
doi = {10.7155/jgaa.00552},
biburl = {http://samuel-mohr.de/files/bib/4.bib},
archivePrefix = {arXiv},
eprint = {2101.03802},
abstract = {A 3-connected graph {$G$} is essentially 4-connected if, for any 3-cut {$S\subseteq V(G)$} of {$G$}, at most one component of {$G-S$} contains at
least two vertices. We prove that every essentially 4-connected maximal planar graph {$G$} on {$n$} vertices contains a cycle of length at least
{$\frac{2}{3}(n+4)$}; moreover, this bound is sharp.}
}