On the Circumference of Essentially 4-connected Planar Graphs Igor Fabrici, Jochen Harant, Samuel Mohr, and Jens M. Schmidt Vol. 24, no. 1, pp. 21-46, 2020. Regular paper. Abstract A planar graph is essentially $4$-connected if it is 3-connected and every of its 3-separators is the neighborhood of a single vertex. Jackson and Wormald proved that every essentially 4-connected planar graph $G$ on $n$ vertices contains a cycle of length at least $\frac{2n+4}{5}$, and this result has recently been improved multiple times. In this paper, we prove that every essentially 4-connected planar graph $G$ on $n$ vertices contains a cycle of length at least $\frac{5}{8}(n+2)$. This improves the previously best-known lower bound $\frac{3}{5}(n+2)$. Submitted: February 2019. Reviewed: August 2019. Revised: September 2019. Accepted: December 2019. Final: December 2019. Published: January 2020. Communicated by Giuseppe Liotta article (PDF) BibTeX