MORE NON-BIPARTITE FORCING PAIRS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113680" target="_blank" >RIV/00216224:14330/19:00113680 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1279</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

MORE NON-BIPARTITE FORCING PAIRS

Popis výsledku v původním jazyce

We study pairs of graphs (H-1, H-2) such that every graph with the densities of H-1 and H-2 close to the densities of H-1 and H-2 in a random graph is quasirandom; such pairs (H-1, H-2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), no. 1, 1-38]: they showed that (K-t, F) is forcing where F is the graph that arises from K-t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma. Vol. 7, 2019] strengthened this result for t = 3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t &gt; 3. We show that [t + 1)/2] doublings always suffice.

Název v anglickém jazyce

MORE NON-BIPARTITE FORCING PAIRS

Popis výsledku anglicky

We study pairs of graphs (H-1, H-2) such that every graph with the densities of H-1 and H-2 close to the densities of H-1 and H-2 in a random graph is quasirandom; such pairs (H-1, H-2) are called forcing. Non-bipartite forcing pairs were first discovered by Conlon, Han, Person and Schacht [Weak quasi-randomness for uniform hypergraphs, Random Structures Algorithms 40 (2012), no. 1, 1-38]: they showed that (K-t, F) is forcing where F is the graph that arises from K-t by iteratively doubling its vertices and edges in a prescribed way t times. Reiher and Schacht [Forcing quasirandomness with triangles, Forum of Mathematics, Sigma. Vol. 7, 2019] strengthened this result for t = 3 by proving that two doublings suffice and asked for the minimum number of doublings needed for t &gt; 3. We show that [t + 1)/2] doublings always suffice.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Acta Mathematica Universitatis Comenianae

ISSN

0231-6986

e-ISSN

0862-9544

Svazek periodika

88

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

7

Strana od-do

819-825

Kód UT WoS článku

000484349000072

EID výsledku v databázi Scopus

2-s2.0-85073799808