# On doubly light vertices in plane graphs

Veronika Kozáková; Tomáš Madaras

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 2, page 333-344
- ISSN: 2083-5892

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topVeronika Kozáková, and Tomáš Madaras. "On doubly light vertices in plane graphs." Discussiones Mathematicae Graph Theory 31.2 (2011): 333-344. <http://eudml.org/doc/270975>.

@article{VeronikaKozáková2011,

abstract = {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.},

author = {Veronika Kozáková, Tomáš Madaras},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {plane graph; doubly light vertex; double light vertex},

language = {eng},

number = {2},

pages = {333-344},

title = {On doubly light vertices in plane graphs},

url = {http://eudml.org/doc/270975},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Veronika Kozáková

AU - Tomáš Madaras

TI - On doubly light vertices in plane graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 2

SP - 333

EP - 344

AB - 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.

LA - eng

KW - plane graph; doubly light vertex; double light vertex

UR - http://eudml.org/doc/270975

ER -

## References

top- [1] O.V. Borodin, Solution of Kotzig-Grünbaum problems on separation of a cycle in planar graphs, Mat. Zametki 46 (1989) 9-12 (in Russian). Zbl0694.05027
- [2] O.V. Borodin, Sharpening Lebesgue's theorem on the structure of lowest faces of convex polytopes, Diskretn. Anal. Issled. Oper., Ser. 1 9, No. 3 (2002) 29-39 (in Russian). Zbl1015.52008
- [3] H. Lebesgue, Quelques consequences simples de la formule d'Euler, J. Math. Pures Appl. 19 (1940) 19-43. Zbl0024.28701
- [4] P. Wernicke, Über den kartographischen Vierfarbensatz, Math. Ann. 58 (1904) 413-426, doi: 10.1007/BF01444968. Zbl35.0511.01
- [5] R. Radoicic and G. Tóth, The discharging method in combinatorial geometry and the Pach-Sharir conjecture, Contemp. Math. 453 (2008) 319-342, doi: 10.1090/conm/453/08806. Zbl1152.05025

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