On long cycles through four prescribed vertices of a polyhedral graph
Jochen Harant, Stanislav Jendrol', Hansjoachim Walther (2008)
Discussiones Mathematicae Graph Theory
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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.