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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1418,
author = {Jochen Harant and Stanislav Jendrol' and Hansjoachim Walther},
title = {On long cycles through four prescribed vertices of a polyhedral graph},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {441-451},
zbl = {1173.05027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1418}
}
Jochen Harant; Stanislav Jendrol'; Hansjoachim Walther. On long cycles through four prescribed vertices of a polyhedral graph. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 441-451. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1418/
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