COOPER, Jacob, Daniel KRÁĽ and TL MARTINS. Finitely forcible graph limits are universal. Advances in Mathematics. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, vol. 340, December, p. 819-854. ISSN 0001-8708. Available from: https://dx.doi.org/10.1016/j.aim.2018.10.019.
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Basic information
Original name Finitely forcible graph limits are universal
Authors COOPER, Jacob (826 United Kingdom of Great Britain and Northern Ireland), Daniel KRÁĽ (203 Czech Republic, guarantor, belonging to the institution) and TL MARTINS.
Edition Advances in Mathematics, SAN DIEGO, ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, 0001-8708.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
Impact factor Impact factor: 1.435
RIV identification code RIV/00216224:14330/18:00106842
Organization unit Faculty of Informatics
Doi http://dx.doi.org/10.1016/j.aim.2018.10.019
UT WoS 000451363700020
Keywords (in Czech) grafové limity; extremální teorie grafů
Keywords in English Graph limits; Extremal graph theory
Tags International impact, Reviewed
Changed by Changed by: RNDr. Pavel Šmerk, Ph.D., učo 3880. Changed: 13/1/2021 11:55.
Abstract
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.
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