On the number of types in sparse graphs

Michał Pilipczuk, Sebastian Siebertz, Szymon Toruńczyk

We prove that for every class of graphs $\mathcal{C}$ which is nowhere dense, as defined by Nesetril and Ossona de Mendez, and for every first order formula $\varphi (\bar{x},\bar{y})$, whe…