Fabrici, IgorIgorFabriciHarant, JochenJochenHarantMohr, SamuelSamuelMohrSchmidt, Jens M.Jens M.Schmidt2020-10-192020-10-192020Discussiones Mathematicae Graph Theory (2020)http://hdl.handle.net/11420/7595A planar 3-connected graph G is called essentially 4-connected if, for every 3-separator S, at least one of the two components of G-S is an isolated vertex. Jackson and Wormald proved that the length circ(G) of a longest cycle of any essentially 4-connected planar graph G on n vertices is at least (2n+4/5) and Fabrici, Harant and Jendrol' improved this result to circ(G)≥ ½(n+4). In the present paper, we prove that an essentially 4-connected planar graph on n vertices contains a cycle of length at least ⅗(n+2) and that such a cycle can be found in time O(n²).en1234-309920201269277circumferenceessentially 4-connected planar graphlongest cycleshortness coefficientMathematics - CombinatoricsMathematics - CombinatoricsComputer Science - Discrete Mathematics05C38, 05C10Journal Article10.7151/dmgt.2133http://arxiv.org/abs/1710.05619v1Other