Dominating sets in planar graphs ∗ Patŕıcia F .

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