Geodesic
Exact stability for Turán's Theorem
Advances in Combinatronics (2021)

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Tur\'an's Theorem says that an extremal $K_{r+1}$-free graph is $r$-partite. The Stability Theorem of Erd\H{o}s and Simonovits shows that if a $K_{r+1}$-free graph with $n$ vertices has close to the maximal $t_r(n)$ edges, then it is close to being $r$-partite. In this paper we determine exactly the $K_{r+1}$-free graphs with at least $m$ edges that are farthest from being $r$-partite, for any $m\ge t_r(n) - \delta_r n^2$. This extends work by Erd\H{o}s, Gy\H{o}ri and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidick\'y and Pfender.
Publié le : 
@article{ADVC_2021_a0,
     author = {D\'aniel Kor\'andi and Alexander Roberts and Alex Scott},
     title = {Exact stability for {Tur\'an's} {Theorem}},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2021_a0/}
}
TY  - JOUR
AU  - Dániel Korándi
AU  - Alexander Roberts
AU  - Alex Scott
TI  - Exact stability for Turán's Theorem
JO  - Advances in Combinatronics
PY  - 2021
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADVC_2021_a0/
LA  - en
ID  - ADVC_2021_a0
ER  - 
%0 Journal Article
%A Dániel Korándi
%A Alexander Roberts
%A Alex Scott
%T Exact stability for Turán's Theorem
%J Advances in Combinatronics
%D 2021
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADVC_2021_a0/
%G en
%F ADVC_2021_a0
Dániel Korándi; Alexander Roberts; Alex Scott. Exact stability for Turán's Theorem. Advances in Combinatronics (2021). http://geodesic.mathdoc.fr/item/ADVC_2021_a0/