@techreport{TR-IC-13-22,
   number = {IC-13-22},
   author = {Patrícia 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.
  }
}