The codegree threshold of K_4-

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
The codegree threshold of K_4-
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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