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@article{1524557,
author = {Cooper, Jacob and Kráľ, Daniel and Martins, TL},
article_location = {SAN DIEGO},
article_number = {December},
doi = {http://dx.doi.org/10.1016/j.aim.2018.10.019},
keywords = {Graph limits; Extremal graph theory},
language = {eng},
issn = {0001-8708},
journal = {Advances in Mathematics},
title = {Finitely forcible graph limits are universal},
url = {https://arxiv.org/abs/1701.03846},
volume = {340},
year = {2018}
}
TY - JOUR
ID - 1524557
AU - Cooper, Jacob - Kráľ, Daniel - Martins, TL
PY - 2018
TI - Finitely forcible graph limits are universal
JF - Advances in Mathematics
VL - 340
IS - December
SP - 819-854
EP - 819-854
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 00018708
KW - Graph limits
KW - Extremal graph theory
UR - https://arxiv.org/abs/1701.03846
L2 - https://arxiv.org/abs/1701.03846
N2 - The theory of graph limits represents large graphs by analytic objects called graphons. Graph limits determined by finitely many graph densities, which are represented by finitely forcible graphons, arise in various scenarios, particularly within extremal combinatorics. Lovasz and Szegedy conjectured that all such graphons possess a simple structure, e.g., the space of their typical vertices is always finite dimensional; this was disproved by several ad hoc constructions of complex finitely forcible graphons. We prove that any graphon is a subgraphon of a finitely forcible graphon. This dismisses any hope for a result showing that finitely forcible graphons possess a simple structure, and is surprising when contrasted with the fact that finitely forcible graphons form a meager set in the space of all graphons. In addition, since any finitely forcible graphon represents the unique minimizer of some linear combination of densities of subgraphs, our result also shows that such minimization problems, which conceptually are among the simplest kind within extremal graph theory, may in fact have unique optimal solutions with arbitrarily complex structure. (C) 2018 Elsevier Inc. All rights reserved.
ER -
COOPER, Jacob, Daniel KRÁĽ a TL MARTINS. Finitely forcible graph limits are universal. \textit{Advances in Mathematics}. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, roč.~340, December, s.~819-854. ISSN~0001-8708. Dostupné z: https://dx.doi.org/10.1016/j.aim.2018.10.019.
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