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pro vyhledávání: '"Griffiths, Simon"'
Autor:
Balister, Paul, Bollobás, Béla, Campos, Marcelo, Griffiths, Simon, Hurley, Eoin, Morris, Robert, Sahasrabudhe, Julian, Tiba, Marius
The $r$-colour Ramsey number $R_r(k)$ is the minimum $n \in \mathbb{N}$ such that every $r$-colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove, for each fixed $r \geqslant 2$, that $$R_
Externí odkaz:
http://arxiv.org/abs/2410.17197
Autor:
Griffiths, Simon, Mattos, Letícia
We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erd\H{o}s-R\'enyi random graph $G(n,p)$. Recently Acan and Kahn showed that the largest such family contains only $O(n^2/(\log{n})^3)$ cliques, with hig
Externí odkaz:
http://arxiv.org/abs/2405.00667
Let $N_{\triangle}(G)$ be the number of triangles in a graph $G$. In [14] and [25] (respectively) the following bounds were proved on the lower tail behaviour of triangle counts in the dense Erd\H{o}s-R\'enyi random graphs $G_m\sim G(n,m)$: \[ \mathb
Externí odkaz:
http://arxiv.org/abs/2403.13792
We consider maximum rooted tree extension counts in random graphs, i.e., we consider M_n = \max_v X_v where X_v counts the number of copies of a given tree in G_{n,p} rooted at vertex v. We determine the asymptotics of M_n when the random graph is no
Externí odkaz:
http://arxiv.org/abs/2310.11661
We consider the question of determining the probability of triangle count deviations in the Erd\H{o}s-R\'enyi random graphs $G(n,m)$ and $G(n,p)$ with densities larger than $n^{-1/2}(\log{n})^{1/2}$. In particular, we determine the log probability $\
Externí odkaz:
http://arxiv.org/abs/2305.04326
The Ramsey number $R(k)$ is the minimum $n \in \mathbb{N}$ such that every red-blue colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove that \[ R(k) \leqslant (4 - \varepsilon)^k \] for
Externí odkaz:
http://arxiv.org/abs/2303.09521
Autor:
Amalova, Akerke1 (AUTHOR) akerke.amalova@gmail.com, Griffiths, Simon2 (AUTHOR) simon.griffiths@jic.ac.uk, Abugalieva, Saule1,3 (AUTHOR) absaule@yahoo.com, Turuspekov, Yerlan1,3 (AUTHOR) yerlant@yahoo.com
Publikováno v:
Agronomy. Aug2024, Vol. 14 Issue 8, p1848. 19p.
Position $n$ points uniformly at random in the unit square $S$, and consider the Voronoi tessellation of $S$ corresponding to the set $\eta$ of points. Toss a fair coin for each cell in the tessellation to determine whether to colour the cell red or
Externí odkaz:
http://arxiv.org/abs/2103.01870