Cut distance identifying graphon parameters over weak* limits

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00556339" target="_blank" >RIV/67985807:_____/22:00556339 - isvavai.cz</a>

Alternative codes found

RIV/67985840:_____/22:00556339

Result on the web

<a href="https://doi.org/10.1016/j.jcta.2022.105615" target="_blank" >https://doi.org/10.1016/j.jcta.2022.105615</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcta.2022.105615" target="_blank" >10.1016/j.jcta.2022.105615</a>

Result language

angličtina

Original language name

Cut distance identifying graphon parameters over weak* limits

Original language description

The theory of graphons comes with the so-called cut norm and the derived cut distance. The cut norm is finer than the weak* topology (when considering the predual of L1-functions). Doležal and Hladký ((2019) [13]) showed, that given a sequence of graphons, a cut distance accumulation graphon can be pinpointed in the set of weak* accumulation points as a minimizer of the entropy. Motivated by this, we study graphon parameters with the property that their minimizers or maximizers identify cut distance accumulation points over the set of weak* accumulation points. We call such parameters cut distance identifying. Of particular importance are cut distance identifying parameters coming from homomorphism densities, t(H,⋅). This concept is closely related to the emerging field of graph norms, and the notions of the step Sidorenko property and the step forcing property introduced by Král', Martins, Pach and Wrochna ((2019) [25]). We prove that a connected graph is weakly norming if and only if it is step Sidorenko, and that if a graph is norming then it is step forcing. Further, we study convexity properties of cut distance identifying graphon parameters, and find a way to identify cut distance limits using spectra of graphons. We also show that continuous cut distance identifying graphon parameters have the <[removed]>, and thus can be used in the proof of the Frieze–Kannan regularity lemma.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Combinatorial Theory. A

ISSN

0097-3165

e-ISSN

1096-0899

Volume of the periodical

189

Issue of the periodical within the volume

July

Country of publishing house

US - UNITED STATES

Number of pages

57

Pages from-to

105615

UT code for WoS article

000793602100001

EID of the result in the Scopus database

2-s2.0-85126595545