Toward characterizing locally common graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00365855" target="_blank" >RIV/68407700:21340/23:00365855 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14330/23:00133882

Výsledek na webu

<a href="http://hdl.handle.net/10467/107798" target="_blank" >http://hdl.handle.net/10467/107798</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/rsa.21099" target="_blank" >10.1002/rsa.21099</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Toward characterizing locally common graphs

Popis výsledku v původním jazyce

A graph H is common if the number of monochromatic copies of H in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of common graphs is one of the most intriguing problems in extremal graph theory. We study the notion of weakly locally common graphs considered by Csoka, Hubai, and Lovasz [arXiv:1912.02926], where the graph is required to be the minimizer with respect to perturbations of the random 2-edge-coloring. We give a complete analysis of the 12 initial terms in the Taylor series determining the number of monochromatic copies of H in such perturbations and classify graphs H based on this analysis into three categories: Graphs of Class I are weakly locally common. Graphs of Class II are not weakly locally common. Graphs of Class III cannot be determined to be weakly locally common or not based on the initial 12 terms. As a corollary, we obtain new necessary conditions on a graph to be common and new sufficient conditions on a graph to be not common.

Název v anglickém jazyce

Toward characterizing locally common graphs

Popis výsledku anglicky

A graph H is common if the number of monochromatic copies of H in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of common graphs is one of the most intriguing problems in extremal graph theory. We study the notion of weakly locally common graphs considered by Csoka, Hubai, and Lovasz [arXiv:1912.02926], where the graph is required to be the minimizer with respect to perturbations of the random 2-edge-coloring. We give a complete analysis of the 12 initial terms in the Taylor series determining the number of monochromatic copies of H in such perturbations and classify graphs H based on this analysis into three categories: Graphs of Class I are weakly locally common. Graphs of Class II are not weakly locally common. Graphs of Class III cannot be determined to be weakly locally common or not based on the initial 12 terms. As a corollary, we obtain new necessary conditions on a graph to be common and new sufficient conditions on a graph to be not common.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Random Structures & Algorithms

ISSN

1042-9832

e-ISSN

1098-2418

Svazek periodika

62

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

38

Strana od-do

181-218

Kód UT WoS článku

000818611200001

EID výsledku v databázi Scopus

2-s2.0-85133300643