On long cycles through four prescribed vertices of a polyhedral graph

For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least [1/36]c+[20/3] through any four vertices of G

Connectivity and Cycles in Graphs

https://digitalcommons.memphis.edu/speccoll-faudreerj/1199/thumbnail.jp