Geodesic
Balanced supersaturation and Turan numbers in random graphs
Advances in Combinatorics (2024)
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In a ground-breaking paper solving a conjecture of Erdős on the number of $n$-vertex graphs not containing a given even cycle, Morris and Saxton \cite{MS} made a broad conjecture on so-called balanced supersaturation property of a bipartite graph $H$. Ferber, McKinley, and Samotij \cite{FMS} established a weaker version of this conjecture and applied it to derive far-reaching results on the enumeration problem of $H$-free graphs. In this paper, we show that Morris and Saxton's conjecture holds under a very mild assumption about $H$, which is widely believed to hold whenever $H$ contains a cycle. We then use our theorem to obtain enumeration results and general upper bounds on the Turán number of a bipartite $H$ in the random graph $G(n,p)$, the latter being first of its kind.
Publié le : 
@article{ADVC_2024_a4,
     author = {Tao Jiang and Sean Longbrake},
     title = {Balanced supersaturation and {Turan} numbers in random graphs},
     journal = {Advances in Combinatorics},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2024_a4/}
}
TY  - JOUR
AU  - Tao Jiang
AU  - Sean Longbrake
TI  - Balanced supersaturation and Turan numbers in random graphs
JO  - Advances in Combinatorics
PY  - 2024
UR  - http://geodesic.mathdoc.fr/item/ADVC_2024_a4/
LA  - en
ID  - ADVC_2024_a4
ER  - 
%0 Journal Article
%A Tao Jiang
%A Sean Longbrake
%T Balanced supersaturation and Turan numbers in random graphs
%J Advances in Combinatorics
%D 2024
%U http://geodesic.mathdoc.fr/item/ADVC_2024_a4/
%G en
%F ADVC_2024_a4
Tao Jiang; Sean Longbrake. Balanced supersaturation and Turan numbers in random graphs. Advances in Combinatorics (2024). http://geodesic.mathdoc.fr/item/ADVC_2024_a4/