Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Grebík, Jan"'
The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was disproved
Externí odkaz:
http://arxiv.org/abs/2408.02151
Autor:
Grebík, Jan, Pikhurko, Oleg
We investigate possible large deviation principles (LDPs) for the $n$-vertex sampling from a given graphon with various speeds $s(n)$ and resolve all the cases except when the speed $s(n)$ is of order $n^2$. For quadratic speed $s=(c+o(1))n^2$, we es
Externí odkaz:
http://arxiv.org/abs/2311.06531
Extending a result of Christiansen, we prove that every mutli-graph $G=(V,E)$ admits a proper edge colouring $\phi:E\to \{1,2,\dots\}$ which is local, that is, $\phi(e)\le \max\{d(x)+\pi(x),d(y)+\pi(y)\}$ for every edge $e$ with end-points $x,y\in V$
Externí odkaz:
http://arxiv.org/abs/2306.04173
Autor:
Grebík, Jan
We prove a full measurable version of Vizing's theorem for bounded degree Borel graphs, that is, we show that every Borel graph $\mathcal{G}$ of degree uniformly bounded by $\Delta\in \mathbb{N}$ defined on a standard probability space $(X,\mu)$ admi
Externí odkaz:
http://arxiv.org/abs/2303.16440
Autor:
Grebík, Jan, Vidnyánszky, Zoltán
We construct bounded degree acyclic Borel graphs with large Borel chromatic number using a graph arising from Ramsey theory and limits of expander sequences.
Externí odkaz:
http://arxiv.org/abs/2205.01839
Autor:
Brandt, Sebastian, Chang, Yi-Jun, Grebík, Jan, Grunau, Christoph, Rozhoň, Václav, Vidnyánszky, Zoltán
We study complexity classes of local problems on regular trees from the perspective of distributed local algorithms and descriptive combinatorics. We show that, surprisingly, some deterministic local complexity classes from the hierarchy of distribut
Externí odkaz:
http://arxiv.org/abs/2204.09329
Let $X$ be a measure space with a measure-preserving action $(g,x) \mapsto g \cdot x$ of an abelian group $G$. We consider the problem of understanding the structure of measurable tilings $F \odot A = X$ of $X$ by a measurable tile $A \subset X$ tran
Externí odkaz:
http://arxiv.org/abs/2203.01511
Autor:
Brandt, Sebastian, Chang, Yi-Jun, Grebík, Jan, Grunau, Christoph, Rozhoň, Václav, Vidnyánszky, Zoltán
Publikováno v:
Forum of Mathematics, Pi 12 (2024) e10
We introduce a new type of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalization of the determinacy method of Marks. The motivation for the constru
Externí odkaz:
http://arxiv.org/abs/2111.03683
Autor:
Grebik, Jan
Following recent result of L. M. T\' oth [arXiv:1906.03137] we show that every $2\Delta$-regular Borel graph $\mathcal{G}$ with a (not necessarily invariant) Borel probability measure admits approximate Schreier decoration. In fact, we show that both
Externí odkaz:
http://arxiv.org/abs/2110.01914
Autor:
Grebík, Jan
In this thesis we consider various questions and problems about graphs that appear in the framework of descriptive set theory. The main object of study are graphons, graphings and variations of the graph G0. We establish an approach to the compactnes
Externí odkaz:
http://www.nusl.cz/ntk/nusl-437544