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@inproceedings{1123297, author = {Ganian, Robert and Hliněný, Petr and Kráľ, Daniel and Obdržálek, Jan and Schwartz, Jarett and Teska, Jakub}, address = {Berlin Heidelberg}, booktitle = {ICALP (2) 2013}, doi = {http://dx.doi.org/10.1007/978-3-642-39212-2_24}, editor = {Fedor V. Fomin, Rusins Freivalds, Marta Z. Kwiatkowska, David Peleg}, keywords = {interval graphs; first-order logic; parameterized complexity}, howpublished = {tištěná verze "print"}, language = {eng}, location = {Berlin Heidelberg}, isbn = {978-3-642-39211-5}, pages = {250-262}, publisher = {Springer}, title = {FO Model Checking of Interval Graphs}, year = {2013} }
TY - JOUR ID - 1123297 AU - Ganian, Robert - Hliněný, Petr - Kráľ, Daniel - Obdržálek, Jan - Schwartz, Jarett - Teska, Jakub PY - 2013 TI - FO Model Checking of Interval Graphs PB - Springer CY - Berlin Heidelberg SN - 9783642392115 KW - interval graphs KW - first-order logic KW - parameterized complexity N2 - 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 this problem 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 some open subset, e.g., in the set (1, 1+epsilon). ER -
GANIAN, Robert, Petr HLINĚNÝ, Daniel KRÁĽ, Jan OBDRŽÁLEK, Jarett SCHWARTZ and Jakub TESKA. FO Model Checking of Interval Graphs. In Fedor V. Fomin, Rusins Freivalds, Marta Z. Kwiatkowska, David Peleg. \textit{ICALP (2) 2013}. Berlin Heidelberg: Springer, 2013, p.~250-262. ISBN~978-3-642-39211-5. Available from: https://dx.doi.org/10.1007/978-3-642-39212-2\_{}24.
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