FO model checking on FO interpretations of nowhere dense classes

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Let C\mathcal{C} be a nowhere dense graph class, and let D\mathcal{D} be a graph class FO interpretable in C\mathcal{C}. FO model-checking conjecture. The class D\mathcal{D} has an FPT algorithm for FO model checking. This conjecture asks whether fixed-parameter tractability of FO model checking extends from nowhere dense classes to all graph classes FO interpretable in them; the source presents it as an explicit conjecture, and no resolution is given.

References

Primary source

Jakub Gajarský, Petr Hliněný, Daniel Lokshtanov, Jan Obdržálek and M. S. Ramanujan, “A New Perspective on FO Model Checking of Dense Graph Classes”, arXiv:1805.01823 (2018).

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