Bounds for the clique cover width of factors of the apex graph of the planar grid (Q2799850)

The clique cover width \(\mathrm{ccw}(G)\) of a graph \(G\) (introduced by the author in [``A new separation theorem with geometric applications'', Preprint, \url{arXiv:1504.04938}]) is the minimum value of the bandwidth of all graphs that are obtained by contracting the cliques in a clique cover of \(G\) into a single vertex. Motivated by a question of \textit{D. R. Wood} [private communication (2015)], the clique cover width is studied on graphs obtained from the \(n\times n\) grid by adding some new vertices, joining each of them to all the vertices of the grid, and possibly adding some edges among the new vertices. Numerous typos, notably missing horizontal bars in fractions (cf. Theorem 2.1 and its proof), do not help in reading the article.