Minimizing NLC-width is NP-complete

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 cliquewidth at most k. In [9] it is shown that a line graph has NLC-width at most k +1 and clique-width at most 2k + 1 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. © Springer-Verlag Berlin Heidelberg 2005.