The codegree threshold of K_4-

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00366791" target="_blank" >RIV/68407700:21340/23:00366791 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/10467/110216" target="_blank" >http://hdl.handle.net/10467/110216</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.12722" target="_blank" >10.1112/jlms.12722</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The codegree threshold of K_4-

Popis výsledku v původním jazyce

The codegree threshold ex_2(n, F) of a 3-graph F is the minimum d = d(n) such that every 3-graph on n vertices in which every pair of vertices is contained in at least d + 1 edges contains a copy of F as a subgraph. We study ex_2(n, F) when F = K_4- , the 3-graph on 4 vertices with 3 edges. Using flag algebra techniques, we prove that if n is sufficiently large, then ex_2(n, K_4-)<= n + 1/ 4 .This settles in the affirmative a conjecture of Nagle [Congressus Numerantium, 1999, pp. 119-128]. In addition, we obtain a stability result: for every near-extremal configuration G, there is a quasirandom tournament T on the same vertex set such that G is o(n^3)-close in the edit distance to the 3-graph C(T) whose edges are the cyclically oriented triangles from T. For infinitely many values of n, we are further able to determine ex_2(n, K_4-) exactly and to show that tournament-based constructions C(T) are extremal for those values of n.

Název v anglickém jazyce

The codegree threshold of K_4-

Popis výsledku anglicky

The codegree threshold ex_2(n, F) of a 3-graph F is the minimum d = d(n) such that every 3-graph on n vertices in which every pair of vertices is contained in at least d + 1 edges contains a copy of F as a subgraph. We study ex_2(n, F) when F = K_4- , the 3-graph on 4 vertices with 3 edges. Using flag algebra techniques, we prove that if n is sufficiently large, then ex_2(n, K_4-)<= n + 1/ 4 .This settles in the affirmative a conjecture of Nagle [Congressus Numerantium, 1999, pp. 119-128]. In addition, we obtain a stability result: for every near-extremal configuration G, there is a quasirandom tournament T on the same vertex set such that G is o(n^3)-close in the edit distance to the 3-graph C(T) whose edges are the cyclically oriented triangles from T. For infinitely many values of n, we are further able to determine ex_2(n, K_4-) exactly and to show that tournament-based constructions C(T) are extremal for those values of n.

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

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

ISSN

0024-6107

e-ISSN

1469-7750

Svazek periodika

107

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

32

Strana od-do

1660-1691

Kód UT WoS článku

000935215000001

EID výsledku v databázi Scopus

2-s2.0-85148342895