Let wₖ be the minimum degree sum of a path on k vertices in a graph. We prove for normal plane maps that: (1) if w₂ = 6, then w₃ may be arbitrarily big, (2) if w₂ < 6, then either w₃ ≤ 18 or there is a ≤ 15-vertex adjacent to two 3-vertices, and (3) if w₂ < 7, then w₃ ≤ 17.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1055,
author = {O.V. Borodin},
title = {Minimal vertex degree sum of a 3-path in plane maps},
journal = {Discussiones Mathematicae Graph Theory},
volume = {17},
year = {1997},
pages = {279-284},
zbl = {0906.05017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1055}
}
O.V. Borodin. Minimal vertex degree sum of a 3-path in plane maps. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 279-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1055/
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