Finitely forcible graph limits are universal

J 2018

Finitely forcible graph limits are universal

COOPER, Jacob; Daniel KRÁĽ a TL MARTINS

Základní údaje

Originální název

Finitely forcible graph limits are universal

Autoři

COOPER, Jacob (826 Velká Británie a Severní Irsko); Daniel KRÁĽ (203 Česká republika, garant, domácí) a TL MARTINS

Vydání

Advances in Mathematics, SAN DIEGO, ACADEMIC PRESS INC ELSEVIER SCIENCE, 2018, 0001-8708

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.435

Kód RIV

RIV/00216224:14330/18:00106842

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1016/j.aim.2018.10.019

UT WoS

000451363700020

EID Scopus

2-s2.0-85055086923

Klíčová slova česky

grafové limity; extremální teorie grafů

Klíčová slova anglicky

Graph limits; Extremal graph theory

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 13. 1. 2021 11:55, RNDr. Pavel Šmerk, Ph.D.

Anotace

V originále

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.

Citovat

COOPER, Jacob; Daniel KRÁĽ a TL MARTINS. Finitely forcible graph limits are universal. 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.

@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.

Přehled o publikaci