Minimizing NLC-width is NP-complete (extended abstract)

We show that a graph has tree-width at most 4k-1 if its line graph has NLC-width or clique-width at most k, and that an incidence graph has tree-width at most k if its line graph has NLC-width or clique-width at most k. In [9] it is shown that a line graph has NLC-width at most k + 2 and clique-width at most 2k + 2 if the root graph has tree-width k. Using these bounds we show by a reduction from tree-width minimization that NLC-width minimization is NP-complete.