D 2023

Forcing Generalized Quasirandom Graphs Efficiently

GRZESIK, Andrzej, Daniel KRÁĽ and Oleg PIKHURKO

Basic information

Original name

Forcing Generalized Quasirandom Graphs Efficiently

Authors

GRZESIK, Andrzej, Daniel KRÁĽ (203 Czech Republic, guarantor, belonging to the institution) and Oleg PIKHURKO

Edition

Brno, European Conference on Combinatorics, Graph Theory and Applications, p. 503-510, 8 pp. 2023

Publisher

MUNI Press

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10101 Pure mathematics

Country of publisher

Czech Republic

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

RIV identification code

RIV/00216224:14330/23:00133884

Organization unit

Faculty of Informatics

ISSN

DOI

Keywords in English

graph limits; quasirandomness; stochastic block model

Tags

International impact, Reviewed
Změněno: 18/4/2024 22:21, RNDr. Pavel Šmerk, Ph.D.

Abstract

V originále

We study generalized quasirandom graphs whose vertex set consists of q parts (of not necessarily the same sizes) with edges within each part and between each pair of parts distributed quasirandomly; such graphs correspond to the stochastic block model studied in statistics and network science. Lovász and Sós showed that the structure of such graphs is forced by homomorphism densities of graphs with at most (10q)^q+q vertices; subsequently, Lovász refined the argument to show that graphs with 4(2q+3)^8 vertices suffice. Our results imply that the structure of generalized quasirandom graphs with q>=2 parts is forced by homomorphism densities of graphs with at most 4q^2-q vertices, and, if vertices in distinct parts have distinct degrees, then 2q+1 vertices suffice. The latter improves the bound of 8q-4 due to Spencer.

Links

MUNI/I/1677/2018, interní kód MU
Name: MUNI AWARD in Science and Humanitites 1 (Acronym: MASH 1)
Investor: Masaryk University, MASH - MUNI Award in Science and Humanities