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.
@article{10_37236_5519,
author = {Micha{\l} Pilipczuk and Szymon Toru\'nczyk},
title = {On ultralimits of sparse graph classes},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/5519},
zbl = {1336.05078},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5519/}
}
TY - JOUR
AU - Michał Pilipczuk
AU - Szymon Toruńczyk
TI - On ultralimits of sparse graph classes
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5519/
DO - 10.37236/5519
ID - 10_37236_5519
ER -
%0 Journal Article
%A Michał Pilipczuk
%A Szymon Toruńczyk
%T On ultralimits of sparse graph classes
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5519/
%R 10.37236/5519
%F 10_37236_5519
Michał Pilipczuk; Szymon Toruńczyk. On ultralimits of sparse graph classes. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/5519
