Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Nie, Jiaxi"'
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
Autor:
Buchanan, Calum, Clifton, Alexander, Culver, Eric, Frankl, Péter, Nie, Jiaxi, Ozeki, Kenta, Rombach, Puck, Yin, Mei
Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order $n$ is covered an odd number of times. In a previous paper with O'Neil
Externí odkaz:
http://arxiv.org/abs/2408.08598
Autor:
Nie, Jiaxi, Spiro, Sam
The random Tur\'an number $\mathrm{ex}(G_{n,p}^r,F)$ is the maximum number of edges in an $F$-free subgraph of the random $r$-uniform hypergraph $G_{n,p}^r$. We prove general results which (informally) shows that if $F$ is an $r_0$-graph, then upper
Externí odkaz:
http://arxiv.org/abs/2408.03406
Autor:
Nie, Jiaxi, Spiro, Sam
Let $\mathrm{ex}(G_{n,p}^r,F)$ denote the maximum number of edges in an $F$-free subgraph of the random $r$-uniform hypergraph $G_{n,p}^r$. Building on recent work of Conlon, Lee, and Sidorenko, we prove non-trivial lower bounds on $\mathrm{ex}(G_{n,
Externí odkaz:
http://arxiv.org/abs/2309.12873
Let $\alpha(\mathbb{F}_q^d,p)$ denote the maximum size of a general position set in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $\alpha(\mathbb{F}_q^2,p)$ up to polylogarithmic factors for all possible values of $p
Externí odkaz:
http://arxiv.org/abs/2309.07744
Autor:
Nie, Jiaxi
The $r$-expansion of a $k$-uniform hypergraph $H$, denoted by $H^{(+r)}$, is an $r$-uniform hypergraph obtained by enlarging each $k$-edge of $H$ with a set of $r-k$ vertices of degree one. The random Tur\'an number $\mathrm{ex}(G^r_{n,p},H)$ is the
Externí odkaz:
http://arxiv.org/abs/2305.04193
Autor:
Nie, Jiaxi
Let $\mathcal{F}$ be a family of $r$-uniform hypergraphs. The random Tur\'an number $\mathrm{ex}(G^r_{n,p},\mathcal{F})$ is the maximum number of edges in an $\mathcal{F}$-free subgraph of $G^r_{n,p}$, where $G^r_{n,p}$ is the Erd\"os-R\'enyi random
Externí odkaz:
http://arxiv.org/abs/2304.14588
Autor:
Frankl, Peter, Nie, Jiaxi
Publikováno v:
Moscow J. Comb. Number Th. 12 (2023) 273-286
An $r$-uniform hypergraph has $(q,p)$-property if any set of $q$ vertices spans a complete sub-hypergraph on $p$ vertices. Let $t_r(n,q,p)$ be the minimum edge density of an $n$-vertex $r$-uniform hypergraph with {\em $(q,p)$-property} and let $t_r(q
Externí odkaz:
http://arxiv.org/abs/2303.00375
Publikováno v:
Journal of Graph Theory 104 (2023), 836-850
A convex geometric graph $G$ is said to be packable if there exist edge-disjoint copies of $G$ in the complete convex geometric graph $K_n$ covering all but $o(n^2)$ edges. We prove that every convex geometric graph with cyclic chromatic number at mo
Externí odkaz:
http://arxiv.org/abs/2207.11624
Autor:
Mulas, Raffaella, Nie, Jiaxi
Publikováno v:
Acta Mathematica Hungarica (2023)
We introduce the following simpler variant of the Tur\'an problem: Given integers $n>k>r\geq 2$ and $m\geq 1$, what is the smallest integer $t$ for which there exists an $r$-uniform hypergraph with $n$ vertices, $t$ edges and $m$ connected components
Externí odkaz:
http://arxiv.org/abs/2207.10052