On long cycles through four prescribed vertices of a polyhedral graph

Harant, Jochen GND; Jendrol', Stanislav GND; Walther, Hansjoachim GND

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.

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