On tripartite common graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00361762" target="_blank" >RIV/68407700:21340/22:00361762 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/10467/105477" target="_blank" >http://hdl.handle.net/10467/105477</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0963548322000074" target="_blank" >10.1017/S0963548322000074</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On tripartite common graphs

Popis výsledku v původním jazyce

This work provides several new classes of tripartite common graphs. A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph K-n is asymptotically minimised by the random colouring. Burr and Rosta, extending a famous conjecture of Erdős, conjectured that every graph is common. The conjectures of Era's and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. The first new class are the so-called triangle trees, which generalises two theorems by Sidorenko and answers a question of Jagger, Šťovíček, and Thomason from 1996. We also prove that, somewhat surprisingly, given any tree T, there exists a triangle tree such that the graph obtained by adding T as a pendant tree is still common. Furthermore, we show that adding arbitrarily many apex vertices to any connected bipartite graph on at most 5 vertices yields a common graph.

Název v anglickém jazyce

On tripartite common graphs

Popis výsledku anglicky

This work provides several new classes of tripartite common graphs. A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph K-n is asymptotically minimised by the random colouring. Burr and Rosta, extending a famous conjecture of Erdős, conjectured that every graph is common. The conjectures of Era's and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. The first new class are the so-called triangle trees, which generalises two theorems by Sidorenko and answers a question of Jagger, Šťovíček, and Thomason from 1996. We also prove that, somewhat surprisingly, given any tree T, there exists a triangle tree such that the graph obtained by adding T as a pendant tree is still common. Furthermore, we show that adding arbitrarily many apex vertices to any connected bipartite graph on at most 5 vertices yields a common graph.

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

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Combinatorics, Probability and Computing

ISSN

0963-5483

e-ISSN

1469-2163

Svazek periodika

31

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

17

Strana od-do

907-923

Kód UT WoS článku

000801041900001

EID výsledku v databázi Scopus

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