## Ganian, Robert and Hlineny, Petr and Kral, Daniel and Obdrzalek, Jan and Schwartz, Jarettet al. - FO Model Checking of Interval Graphs

lmcs:1612 - Logical Methods in Computer Science, December 14, 2015, Volume 11, Issue 4
FO Model Checking of Interval Graphs

Authors: Ganian, Robert and Hlineny, Petr and Kral, Daniel and Obdrzalek, Jan and Schwartz, Jarett and Teska, Jakub

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 $(1, 1 + \varepsilon)$.

Source : oai:arXiv.org:1302.6043
DOI : 10.2168/LMCS-11(4:11)2015
Volume: Volume 11, Issue 4
Published on: December 14, 2015
Submitted on: March 3, 2015
Keywords: Computer Science - Discrete Mathematics,Computer Science - Logic in Computer Science