The domination number of plane triangulations

Abstract We introduce a class of plane graphs called weak near-triangulations, and prove that this class is closed under certain graph operations. Then we use the properties of weak near-triangulations to prove that every plane triangulation on n > 6 vertices has a dominating set of size at most 17 n / 53 . This improves the bound n / 3 obtained by Matheson and Tarjan.