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.
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Gurski, F., Wanke, E. (2005). Minimizing NLC-Width is NP-Complete. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_7
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DOI: https://doi.org/10.1007/11604686_7
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