Balanced supersaturation and Turan numbers in random graphs
Advances in Combinatronics (2024)
Voir la notice de l'article provenant de la source Advances in Combinatronics website
In a ground-breaking paper solving a conjecture of Erd\H{o}s 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 Tur\'an 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 Combinatronics},
publisher = {mathdoc},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADVC_2024_a4/}
}
Tao Jiang; Sean Longbrake. Balanced supersaturation and Turan numbers in random graphs. Advances in Combinatronics (2024). http://geodesic.mathdoc.fr/item/ADVC_2024_a4/