FO Model Checking of Interval Graphs

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Authors

GANIAN Robert HLINĚNÝ Petr KRÁĽ Daniel OBDRŽÁLEK Jan SCHWARTZ Jarett TESKA Jakub

Year of publication 2015
Type Article in Periodical
Magazine / Source Logical Methods in Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web http://arxiv.org/pdf/1302.6043.pdf
Doi http://dx.doi.org/10.2168/LMCS-11(4:11)2015
Field Informatics
Keywords rst-order model checking; parameterized complexity; interval graph; clique-width
Description 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 + µ).
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