Zobrazeno 1 - 10
of 4 686
pro vyhledávání: '"A Sudakov"'
More than 40 years ago, Galvin, Rival and Sands showed that every $K_{s, s}$-free graph containing an $n$-vertex path must contain an induced path of length $f(n)$, where $f(n)\to \infty$ as $n\to \infty$. Recently, it was shown by Duron, Esperet and
Externí odkaz:
http://arxiv.org/abs/2411.19173
Autor:
Smirnov, V. N., Kazistova, K. M., Sudakov, I. A., Leplat, V., Gasnikov, A. V., Lobanov, A. V.
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar to other
Externí odkaz:
http://arxiv.org/abs/2411.15866
We study and solve several problems in two closely related settings: set families in $2^{[n]}$ with many disjoint pairs of sets and low rank matrices with many zero entries. - More than 40 years ago, Daykin and Erd\H{o}s asked for the maximum number
Externí odkaz:
http://arxiv.org/abs/2411.13510
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of non-linear
Externí odkaz:
http://arxiv.org/abs/2410.19075
The canonical Ramsey theorem of Erd\H{o}s and Rado implies that for any graph $H$, any edge-coloring (with an arbitrary number of colors) of a sufficiently large complete graph $K_N$ contains a monochromatic, lexicographic, or rainbow copy of $H$. Th
Externí odkaz:
http://arxiv.org/abs/2410.08644
In 1992, Erd\H{o}s and Hajnal posed the following natural problem: Does there exist, for every $r\in \mathbb{N}$, an integer $F(r)$ such that every graph with chromatic number at least $F(r)$ contains $r$ edge-disjoint cycles on the same vertex set?
Externí odkaz:
http://arxiv.org/abs/2410.02437
For two graphs $F,H$ and a positive integer $n$, the function $f_{F,H}(n)$ denotes the largest $m$ such that every $H$-free graph on $n$ vertices contains an $F$-free induced subgraph on $m$ vertices. This function has been extensively studied in the
Externí odkaz:
http://arxiv.org/abs/2409.06650
We study the amount of maximal extractable value (MEV) captured by validators, as a function of searcher competition, in blockchains with competitive block building markets such as Ethereum. We argue that the core is a suitable solution concept in th
Externí odkaz:
http://arxiv.org/abs/2407.07474
A graph $G$ is said to be $p$-locally dense if every induced subgraph of $G$ with linearly many vertices has edge density at least $p$. A famous conjecture of Kohayakawa, Nagle, R\"odl, and Schacht predicts that locally dense graphs have, asymptotica
Externí odkaz:
http://arxiv.org/abs/2406.12418
The celebrated Erd\H{o}s-Hajnal conjecture says that any graph without a fixed induced subgraph $H$ contains a very large homogeneous set. A direct analog of this conjecture is not true for hypergraphs. In this paper we present two natural variants o
Externí odkaz:
http://arxiv.org/abs/2406.04154