Geodesic
The Ramsey number of books
Advances in Combinatorics (2019) Cet article a éte moissonné depuis la source Scholastica

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We show that in every two-colouring of the edges of the complete graph $K_N$ there is a monochromatic $K_k$ which can be extended in at least $(1 + o_k(1))2^{-k}N$ ways to a monochromatic $K_{k+1}$. This result is asymptotically best possible, as may be seen by considering a random colouring. Equivalently, defining the book $B_n^{(k)}$ to be the graph consisting of $n$ copies of $K_{k+1}$ all sharing a common $K_k$, we show that the Ramsey number $r(B_n^{(k)}) = 2^k n + o_k(n)$. In this form, our result answers a question of Erdős, Faudree, Rousseau and Schelp and establishes an asymptotic version of a conjecture of Thomason.
Publié le : 
@article{ADVC_2019_a2,
     author = {David Conlon},
     title = {The {Ramsey} number of books},
     journal = {Advances in Combinatorics},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2019_a2/}
}
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AU  - David Conlon
TI  - The Ramsey number of books
JO  - Advances in Combinatorics
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/ADVC_2019_a2/
LA  - en
ID  - ADVC_2019_a2
ER  - 
%0 Journal Article
%A David Conlon
%T The Ramsey number of books
%J Advances in Combinatorics
%D 2019
%U http://geodesic.mathdoc.fr/item/ADVC_2019_a2/
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%F ADVC_2019_a2
David Conlon. The Ramsey number of books. Advances in Combinatorics (2019). http://geodesic.mathdoc.fr/item/ADVC_2019_a2/