Geodesic
On long cycles through four prescribed vertices of a polyhedral graph
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 441-451.

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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.
Keywords: graph, long cycle, prescribed vertices 
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Harant, Jochen; Jendrol', Stanislav; Walther, Hansjoachim. On long cycles through four prescribed vertices of a polyhedral graph. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 441-451. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a4/

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