@techreport{TR-IC-13-22, number = {IC-13-22}, author = {PatrĂ­cia F. Hongo and C. N. Campos}, title = {{Dominating sets in planar graphs}}, month = {September}, year = {2013}, institution = {Institute of Computing, University of Campinas}, note = {In English, 18 pages. \par\selectlanguage{english}\textbf{Abstract} A dominating set of a graph $G$ is a subset $D\subseteq V(G)$ 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 $\gamma(G)$. In 1996, Tarjan and Matheson proved that $\gamma(G)\leq n/3$ for triangulated discs and conjectured that $\gamma(G) \leq n/4$ for triangulated planar graphs with sufficiently large $n$. In the present work, we verify the conjecture for two simple classes of triangulated planar graphs. } }