Circumference of essentially 4-connected planar triangulations - Fabrici, Igor; Harant, Jochen; Mohr, Samuel; Schmidt, Jens (Journal of Graph Algorithms and Applications, 2021)
A 3-connected graph G is essentially 4-connected if, for any 3-cut SV(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 23(n+4); moreover, this bound is sharp.