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of 102
pro vyhledávání: '"Cherkashin, D."'
Autor:
Cherkashin, D., Teplitskaya, Y.
We consider a general metric Steiner problem which is of finding a set $\mathcal{S}$ with minimal length such that $\mathcal{S} \cup A$ is connected, where $A$ is a given compact subset of a given complete metric space $X$; a solution is called Stein
Externí odkaz:
http://arxiv.org/abs/2302.02189
Publikováno v:
Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)518(2022), 94-113
We prove that for an arbitrary $\varepsilon > 0$ holds \[ \chi (\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $\chi(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of mo
Externí odkaz:
http://arxiv.org/abs/2208.02230
\emph{A maximal distance minimizer} for a given compact set $M \subset \mathbb{R}^2$ and some given $r > 0$ is a set having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R}^2$ s
Externí odkaz:
http://arxiv.org/abs/2106.00809
Fix a compact $M \subset \mathbb{R}^2$ and $r>0$. A minimizer of the maximal distance functional is a connected set $\Sigma$ of the minimal length, such that \[ max_{y \in M} dist(y,\Sigma) \leq r. \] The problem of finding maximal distance minimizer
Externí odkaz:
http://arxiv.org/abs/2011.10463
For a positive integer $n>1$ denote by $\omega(n)$ the maximal possible number $k$ of different functions $f_1,\dots,f_k:\mathbb{Z}/n\mathbb{Z}\mapsto \mathbb{Z}/n\mathbb{Z}$ such that each function $f_i-f_j,i
Externí odkaz:
http://arxiv.org/abs/1901.00440
Publikováno v:
Algebra i Analiz, 2017, Volume 29, Issue 5, Pages 68--89
We consider natural generalization of plane chromatic number problem. We consider chromatic numbers $\chi$ of spaces $\mathbb{R}^n \times [0,\varepsilon]^k$ for arbitrary small $\varepsilon$. We prove that $5 \leq\chi(\mathbb{R}^2\times [0,\varepsilo
Externí odkaz:
http://arxiv.org/abs/1512.06444
Publikováno v:
Zeitschrift für Arabische Linguistik, 2019 Jan 01(69), 61-93.
Externí odkaz:
https://www.jstor.org/stable/10.13173/zeitarabling.69.0061
Publikováno v:
Zeitschrift für Arabische Linguistik, 2019 Jan 01(70), 73-91.
Externí odkaz:
https://www.jstor.org/stable/10.13173/zeitarabling.70.0073
In 1973 P. Erd\H{o}s and L. Lov\'asz noticed that any hypergraph whose edges are pairwise intersecting has chromatic number 2 or 3. In the first case, such hypergraph may have any number of edges. However, Erd\H{o}s and Lov\'asz proved that in the se
Externí odkaz:
http://arxiv.org/abs/1110.1756
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