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@article{1486962, author = {Hliněný, Petr and Pokrývka, Filip and Roy, Bodhayan}, article_location = {Amsterdam}, article_number = {1}, doi = {http://dx.doi.org/10.1016/j.comgeo.2018.10.001}, keywords = {first-order logic; model checking; fixed-parameter tractability; intersec- tion graphs; visibility graphs}, language = {eng}, issn = {0925-7721}, journal = {Computational geometry}, title = {FO model checking on geometric graphs}, url = {http://dx.doi.org/10.1016/j.comgeo.2018.10.001}, volume = {78}, year = {2019} }
TY - JOUR ID - 1486962 AU - Hliněný, Petr - Pokrývka, Filip - Roy, Bodhayan PY - 2019 TI - FO model checking on geometric graphs JF - Computational geometry VL - 78 IS - 1 SP - 1-19 EP - 1-19 PB - ELSEVIER SCIENCE BV SN - 09257721 KW - first-order logic KW - model checking KW - fixed-parameter tractability KW - intersec- tion graphs KW - visibility graphs UR - http://dx.doi.org/10.1016/j.comgeo.2018.10.001 N2 - Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of dense classes of graphs or other structures. We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking of posets of bounded width. We also complement the tractability results by related hardness reductions. ER -
HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY. FO model checking on geometric graphs. \textit{Computational geometry}. Amsterdam: ELSEVIER SCIENCE BV, 2019, vol.~78, No~1, p.~1-19. ISSN~0925-7721. Available from: https://dx.doi.org/10.1016/j.comgeo.2018.10.001.
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