Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Frankl, Nóra"'
Autor:
Balko, Martin, Frankl, Nóra
The celebrated Szemer\'edi--Trotter theorem states that the maximum number of incidences between $n$ points and $n$ lines in the plane is $O(n^{4/3})$, which is asymptotically tight. Solymosi (2005) conjectured that for any set of points $P_0$ and fo
Externí odkaz:
http://arxiv.org/abs/2409.00954
Two celebrated extensions of Helly's theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of B\'ar\'any, Katchalski, and Pach (1982). Improving on several recent works, we prove an optimal combinat
Externí odkaz:
http://arxiv.org/abs/2402.12268
We prove that for any $\ell_p$-norm in the plane with $1
Externí odkaz:
http://arxiv.org/abs/2308.08840
Answering a question by Letzter and Snyder, we prove that for large enough $k$ any $n$-vertex graph $G$ with minimum degree at least $\frac{1}{2k-1}n$ and without odd cycles of length less than $2k+1$ is $3$-colourable. In fact, we prove a stronger r
Externí odkaz:
http://arxiv.org/abs/2302.01875
Given a set $S \subseteq \mathbb{R}^2$, define the \emph{Helly number of $S$}, denoted by $H(S)$, as the smallest positive integer $N$, if it exists, for which the following statement is true: for any finite family $\mathcal{F}$ of convex sets in~$\m
Externí odkaz:
http://arxiv.org/abs/2301.04683
Publikováno v:
Proceedings of the American Mathematical Society, 2023, Vol. 151, No. 6, pp. 2353--2362
In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conjecture and relate it to several other problems in combinatorics.
Com
Com
Externí odkaz:
http://arxiv.org/abs/2203.03873
Autor:
Frankl, Nora, Woodruff, Dora
A recent generalization of the Erd\H{o}s Unit Distance Problem, proposed by Palsson, Senger and Sheffer, asks for the maximum number of unit distance paths with a given number of vertices in the plane and in $3$-space. Studying a variant of this ques
Externí odkaz:
http://arxiv.org/abs/2202.02919
Autor:
Frankl, Nora, Kupavskii, Andrey
Erd\H{o}s and Purdy, and later Agarwal and Sharir, conjectured that any set of $n$ points in $\mathbb R^{d}$ determine at most $Cn^{d/2}$ congruent $k$-simplices for even $d$. We obtain the first significant progress towards this conjecture, showing
Externí odkaz:
http://arxiv.org/abs/2112.10245
Publikováno v:
European Journal of Combinatorics, 2024, Vol. 118, 103918, 27 pp
Given a metric space $\mathcal{M}$ that contains at least two points, the chromatic number $\chi\left(\mathbb{R}^n_{\infty}, \mathcal{M} \right)$ is defined as the minimum number of colours needed to colour all points of an $n$-dimensional space $\ma
Externí odkaz:
http://arxiv.org/abs/2111.08949
Publikováno v:
In European Journal of Combinatorics May 2024 118
