On Ultralimits of Sparse Graph Classes

  • Michał Pilipczuk
  • Szymon Toruńczyk
Keywords: Nowhere denseness, Quasi-wideness, Splitter game, Ultraproduct


The notion of nowhere denseness is one of the central concepts of the recently developed theory of sparse graphs. We study the properties of nowhere dense graph classes by investigating appropriate limit objects defined using the ultraproduct construction. It appears that different equivalent definitions of nowhere denseness, for example via quasi-wideness or the splitter game, correspond to natural notions for the limit objects that are conceptually simpler and allow for less technically involved reasonings.
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