FO Model Checking of Interval Graphs

Robert Ganian, Petr Hlineny, Daniel Kral, Jan Obdrzalek, Jarett Schwartz, Jakub Teska, Martin Grohe
2015 Logical Methods in Computer Science  
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
more » ... t is dense in an open subset, e.g., in the set (1, 1 + ε).
doi:10.2168/lmcs-11(4:11)2015 fatcat:o4p2ujoglbhf5hgaiqmesbi25y