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.
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Pergel, M. (2007). Recognition of Polygon-Circle Graphs and Graphs of Interval Filaments Is NP-Complete. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_23
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DOI: https://doi.org/10.1007/978-3-540-74839-7_23
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