@techreport{TR-IC-99-14,
  number = {IC-99-14},
  author = {Cândido F. Xavier de Mendonça and Erico F. Xavier and Luerbio Faria and Celina M. H. de Figueiredo and Jorge Stolfi},
  title = {The Vertex Deletion Number of {$C_n \times C_m$}},
  month = {May},
  year = {1999}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 39 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      The vertex deletion number of a graph $G$ is the smallest
      integer $k \geq 0$ such that there is a planar induced subgraph
      of $G$ obtained by the removal of $k$ vertices from $G$.
      In this work we study the vertex deletion number of 
      $C_n\times C_m$, the rectangular grid with toroidal topology.
      We prove the extact result $\min\{n,m\} - \xi_{5,9}(n,m)$,
      where $\xi_{i,j}(k_1,k_2)$ is the number of true conditions
      among the following: (i) $k_1 = k_2 \leq i$ and 
      (ii) $k_1 + k_2 \leq j$.
  }
}