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Dominating Sets in Planar Graphs

✍ Scribed by Lesley R. Matheson; Robert E. Tarjan

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 174 KB
Volume: 17
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1996.0048

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## Abstract Let __G__ be a graph and let __S__⊂__V__(__G__). We say that __S__ is __dominating__ in __G__ if each vertex of __G__ is in __S__ or adjacent to a vertex in __S__. We show that every triangulation on the torus and the Klein bottle with __n__ vertices has a dominating set of cardinality