Discussiones Mathematicae Graph Theory 31(2) (2011) 333-344
doi: 10.7151/dmgt.1549

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ON DOUBLY LIGHT VERTICES IN PLANE GRAPHS

Veronika Kozáková  and  Tomás Madaras

Institute of Mathematics, Faculty of Sciences
University of P.J. Safárik
Jesenná 5, 041 54 Košice, Slovak Republic

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.

Keywords: plane graph, doubly light vertex.

2010 Mathematics Subject Classification: 05C10.

References

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Received 16 November 2009
Revised 3 June 2010
Accepted 9 June 2010