A vertex is said to be doubly light in a family of plane graphs if its degree and sizes of neighbouring faces are bounded above by a finite constant. We provide several results on the existence of doubly light vertices in various families of plane graph.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1549,
author = {Veronika Koz\'akov\'a and Tom\'a\v s Madaras},
title = {On doubly light vertices in plane graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {31},
year = {2011},
pages = {333-344},
zbl = {1227.05132},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1549}
}
Veronika Kozáková; Tomáš Madaras. On doubly light vertices in plane graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 333-344. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1549/
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