Minimizing nLC-width is nP-complete

Authors:
Frank Gurski;Egon Wanke
Affiliations:
Institute of Computer Science, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany;Institute of Computer Science, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany
Venue:
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Year:
2005

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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.