Circumference of essentially 4-connected planar triangulations

@article{Fabrici2021CircumferenceOE,
  title={Circumference of essentially 4-connected planar triangulations},
  author={Igor Fabrici and Jochen Harant and Samuel Mohr and Jens M. Schmidt},
  journal={J. Graph Algorithms Appl.},
  year={2021},
  volume={25},
  pages={121-132}
}
A 3-connected graph G is essentially 4-connected if, for any 3-cut S ⊆ 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 2 3 (n+ 4); moreover, this bound is sharp. 
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