Open this publication in new window or tab >>2023 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 107, no 5, p. 1660-1691Article in journal (Refereed) Published
Abstract [en]
The codegree threshold ex2 (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 ex2 (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
ex2 (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(n3)-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 ex2(n, K-4) exactly and to show that tournament-based constructions C(T) are extremal for those values of n.
Place, publisher, year, edition, pages
John Wiley & Sons, 2023
National Category
Discrete Mathematics
Identifiers
urn:nbn:se:umu:diva-205362 (URN)10.1112/jlms.12722 (DOI)000935215000001 ()2-s2.0-85148342895 (Scopus ID)
Funder
EU, European Research Council, 101020255Swedish Research Council, 2016‐03488Swedish Research Council, 2021‐03687
2023-03-292023-03-292023-07-14Bibliographically approved