Recognition of polygon-circle graphs and graphs of interval filaments is NP-complete

Authors:
Martin Pergel
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 1, Czech Republic
Venue:
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Year:
2007

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Abstract

Polygon-circle graphs (PC-graphs) are defined as intersection graphs of polygons inscribed into a circle, graphs of interval filaments (IFA-graphs) are intersection graphs of curves with both endpoints on prescribed line (filament), filaments above two disjoint intervals must not intersect each other. Recognition of these classes has been a long outstanding open problem. We prove that it is NP-complete to recognize both classes.