# Dominating sets in planar graphs ∗ Patŕıcia F .

@inproceedings{Hongo2013DominatingSI, title={Dominating sets in planar graphs ∗ Patŕıcia F .}, author={Hongo and Claudia L Campos}, year={2013} }

- Published 2013

A dominating set of a graph G is a subset D ⊆ V (G) such that each vertex of G is in D or is adjacent to a vertex in D. The cardinality of a minimum size dominating set for G is denoted by γ(G). In 1996, Tarjan and Matheson proved that γ(G) ≤ n/3 for triangulated discs and conjectured that γ(G) ≤ n/4 for triangulated planar graphs with sufficiently large n. In the present work, we verify the conjecture for two simple classes of triangulated planar graphs.

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