@techreport{men-xav-sto-far-fig-99-vdst-tr,
  author = {C{\^a}ndido F. Xavier de {Mendon{\c{c}}a Neto} and {\'E}rico F. Xavier and Lu{\'e}rbio Faria and Celina M. H. de Figueiredo and Jorge Stolfi},
  title = {The Vertex Deletion Number and Splitting Number of a Triangulation of {$C_n \times C_m$}},
  institution = {Institute of Computing, Univ. of Campinas},
  number = {IC-99-15},
  pages = {8},
  year = 1999,
  month = jun,
  abstract = {The vertex deletion number $\phi(G)$ of a graph $G$ is the minimum number of vertices that must be deleted from $G$ to produce a planar graph. The splitting number $\sigma(G)$ of $G$ is the smallest number of vertex splitting operations that must be applied to $G$ to make it planar. Here we determine these topological invariants for the graph family ${\cal T}_{C_n \times C_m}$, a regular triangulation of the torus obtained by adding parallel diagonal edges to the faces of the rectangular toroidal grid $C_n \times C_m$. Specifically, we prove that the obvious upper bound $\phi = \sigma = \min\{n,m\}$ is also a lower bound.}
}