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pro vyhledávání: '"ZENG, Ji"'
Autor:
Suk, Andrew, Zeng, Ji
The monotone path $P_{n+2}$ is an ordered 3-uniform hypergraph whose vertex set has size $n+2$ and edge set consists of all consecutive triples. In this note, we consider the collection $\mathcal{J}_n$ of ordered 3-uniform hypergraphs named monotone
Externí odkaz:
http://arxiv.org/abs/2411.15649
For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for every set o
Externí odkaz:
http://arxiv.org/abs/2406.08913
In this paper, we consider saturation problems related to the celebrated Erd\H{o}s--Szekeres convex polygon problem. For each $n \ge 7$, we construct a planar point set of size $(7/8) \cdot 2^{n-2}$ which is saturated for convex $n$-gons. That is, th
Externí odkaz:
http://arxiv.org/abs/2312.01223
Autor:
Suk, Andrew, Zeng, Ji
As a variant of the celebrated Szemer\'edi--Trotter theorem, Guth and Katz proved that $m$ points and $n$ lines in $\mathbb{R}^3$ with at most $\sqrt{n}$ lines in a common plane must determine at most $O(m^{1/2}n^{3/4})$ incidences for $n^{1/2}\leq m
Externí odkaz:
http://arxiv.org/abs/2311.04804
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:
Zeng, Ji
We prove that every $n$-vertex complete simple topological graph generates at least $\Omega(n)$ pairwise disjoint $4$-faces. This improves upon a recent result by Hubard and Suk. As an immediate corollary, every $n$-vertex complete simple topological
Externí odkaz:
http://arxiv.org/abs/2308.04742
Autor:
Suk, Andrew, Zeng, Ji
A finite point set in $\mathbb{R}^d$ is in general position if no $d + 1$ points lie on a common hyperplane. Let $\alpha_d(N)$ be the largest integer such that any set of $N$ points in $\mathbb{R}^d$ with no $d + 2$ members on a common hyperplane, co
Externí odkaz:
http://arxiv.org/abs/2211.15968
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
Publikováno v:
Electronic Journal of Combinatorics 30 (2023), P4.32
Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors exactly $n$
Externí odkaz:
http://arxiv.org/abs/2207.11272
Autor:
Suk, Andrew, Zeng, Ji
We show that every complete $n$-vertex simple topological graph contains a topological subgraph on at least $(\log n)^{1/4 - o(1)}$ vertices that is weakly isomorphic to the complete convex geometric graph or the complete twisted graph. This is the f
Externí odkaz:
http://arxiv.org/abs/2204.04293