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VOLUME 11, ISSUE 4, PAPER 11


FO Model Checking of Interval Graphs

©Robert Ganian, Vienna University of Technology
©Petr Hlineny, Masaryk University, Brno
©Daniel Kral, University of Warwick
©Jan Obdrzalek, Masaryk University, Brno
©Jarett Schwartz, UC Berkeley
©Jakub Teska, University of West Bohemia, Pilsen

Abstract
We study the computational complexity of the FO model checking problem on interval graphs, i.e., intersection graphs of intervals on the real line. The main positive result is that FO model checking and successor-invariant FO model checking can be solved in time O(n log n) for n-vertex interval graphs with representations containing only intervals with lengths from a prescribed finite set. We complement this result by showing that the same is not true if the lengths are restricted to any set that is dense in an open subset, e.g., in the set (1, 1 + ε).

Publication date: December 14, 2015

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-11(4:11)2015

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