Zobrazeno 1 - 10
of 1 227
pro vyhledávání: '"Mubayi, A."'
Autor:
Chakravarty, Sayok, Mubayi, Dhruv
Fix an integer $s \ge 2$. Let $\mathcal{P}$ be a set of $n$ points and let $\mathcal{L}$ be a set of lines in a linear space such that no line in $\mathcal{L}$ contains more than $(n-1)/(s-1)$ points of $\mathcal{P}$. Suppose that for every $s$-set $
Externí odkaz:
http://arxiv.org/abs/2411.14634
Autor:
Conlon, David, Fox, Jacob, Gunby, Benjamin, He, Xiaoyu, Mubayi, Dhruv, Suk, Andrew, Verstraëte, Jacques, Yu, Hung-Hsun Hans
A natural open problem in Ramsey theory is to determine those $3$-graphs $H$ for which the off-diagonal Ramsey number $r(H, K_n^{(3)})$ grows polynomially with $n$. We make substantial progress on this question by showing that if $H$ is tightly conne
Externí odkaz:
http://arxiv.org/abs/2411.13812
For a $k$-uniform hypergraph $F$ and a positive integer $n$, the Ramsey number $r(F,n)$ denotes the minimum $N$ such that every $N$-vertex $F$-free $k$-uniform hypergraph contains an independent set of $n$ vertices. A hypergraph is $\textit{slowly gr
Externí odkaz:
http://arxiv.org/abs/2409.01442
Recent work showing the existence of conflict-free almost-perfect hypergraph matchings has found many applications. We show that, assuming certain simple degree and codegree conditions on the hypergraph $ \mathcal{H} $ and the conflicts to be avoided
Externí odkaz:
http://arxiv.org/abs/2407.18144
Autor:
Mubayi, Dhruv, Verstraete, Jacques
Let $f_{F,G}(n)$ be the largest size of an induced $F$-free subgraph that every $n$-vertex $G$-free graph is guaranteed to contain. We prove that for any triangle-free graph $F$, \[ f_{F,K_3}(n) = f_{K_2,K_3}(n)^{1 + o(1)} = n^{\frac{1}{2} + o(1)}.\]
Externí odkaz:
http://arxiv.org/abs/2407.03121
Let $ES_{\ell}(n)$ be the minimum $N$ such that every $N$-element point set in the plane contains either $\ell$ collinear members or $n$ points in convex position. We prove that there is a constant $C>0$ such that, for each $\ell, n \ge 3$, $$ (3\ell
Externí odkaz:
http://arxiv.org/abs/2405.03455
Fix $k\ge 11$ and a rainbow $k$-clique $R$. We prove that the inducibility of $R$ is $k!/(k^k-k)$. An extremal construction is a balanced recursive blow-up of $R$. This answers a question posed by Huang, that is a generalization of an old problem of
Externí odkaz:
http://arxiv.org/abs/2405.03112
Autor:
Conlon, David, Fox, Jacob, He, Xiaoyu, Mubayi, Dhruv, Pham, Huy Tuan, Suk, Andrew, Verstraëte, Jacques
Answering a question of Erd\H{o}s and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit const
Externí odkaz:
http://arxiv.org/abs/2404.16016
Autor:
Conlon, David, Fox, Jacob, Gunby, Benjamin, He, Xiaoyu, Mubayi, Dhruv, Suk, Andrew, Verstraete, Jacques
A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r(H, K_n^{(3)})$ of a fixed $3$-uniform hypergraph $H$ versus the complete $3$-uniform hypergraph with $n$ vertices. We study this problem, p
Externí odkaz:
http://arxiv.org/abs/2404.02021
Autor:
Cairncross, Emily, Mubayi, Dhruv
We consider three extremal problems about the number of copies of a fixed graph in another larger graph. First, we correct an error in a result of Reiher and Wagner and prove that the number of $k$-edge stars in a graph with density $x \in [0, 1]$ is
Externí odkaz:
http://arxiv.org/abs/2403.12016