On Ultralimits of Sparse Graph Classes
Copyright policy )On Ultralimits of Sparse Graph Classes
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.
- University of Warsaw Poland
FOS: Computer and information sciences, quasi-wideness, Discrete Mathematics (cs.DM), nowhere denseness, splitter game, ultraproduct, Ultraproducts and related constructions, FOS: Mathematics, Mathematics - Combinatorics, Density (toughness, etc.), Combinatorics (math.CO), Computer Science - Discrete Mathematics
FOS: Computer and information sciences, quasi-wideness, Discrete Mathematics (cs.DM), nowhere denseness, splitter game, ultraproduct, Ultraproducts and related constructions, FOS: Mathematics, Mathematics - Combinatorics, Density (toughness, etc.), Combinatorics (math.CO), Computer Science - Discrete Mathematics
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