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Akademický článek
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Berge equilibrium in the sense of Zhukovskii (Berge-Zhukovskii) is an alternate solution concept in non-cooperative game theory that formalizes cooperation in a noncooperative setting. In this paper the epsilon-Berge-Zhukovskii equilibrium is introdu
Externí odkaz:
http://arxiv.org/abs/1405.0355
Autor:
Verbitsky, Oleg, Zhukovskii, Maksim
We show that if $p=O(1/n)$, then the Erd\H{o}s-R\'{e}nyi random graph $G(n,p)$ with high probability admits a canonical labeling computable in time $O(n\log n)$. Combined with the previous results on the canonization of random graphs, this implies th
Externí odkaz:
http://arxiv.org/abs/2409.18109
We prove that the density of any covering single-insertion code $C\subseteq X^r$ over the $n$-symbol alphabet $X$ cannot be smaller than $1/r+\delta_r$ for some positive real $\delta_r$ not depending on $n$. This improves the volume lower bound of $1
Externí odkaz:
http://arxiv.org/abs/2409.06425
We say that a vertex $v$ in a connected graph $G$ is decisive if the numbers of walks from $v$ of each length determine the graph $G$ rooted at $v$ up to isomorphism among all connected rooted graphs with the same number of vertices. On the other han
Externí odkaz:
http://arxiv.org/abs/2409.03690
Asymptotic behaviour of maximum sizes of induced trees and forests has been studied extensively in last decades, though the overall picture is far from being complete. In this paper, we close several significant gaps: 1) We prove $2$-point concentrat
Externí odkaz:
http://arxiv.org/abs/2408.15215
Publikováno v:
International Journal of Geometric Methods in Modern Physics, Vol. 6, No. 8, (2009)
We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination
Externí odkaz:
http://arxiv.org/abs/0912.1875
Autor:
Terekhov, Nikolai, Zhukovskii, Maksim
Given a graph $F$ and a positive integer $n$, the weak $F$-saturation number $\mathrm{wsat}(K_n,F)$ is the minimum number of edges in a graph $H$ on $n$ vertices such that the edges missing in $H$ can be added, one at a time, so that every edge creat
Externí odkaz:
http://arxiv.org/abs/2405.17857
Autor:
Hershko, Tal, Zhukovskii, Maksim
We study the problem of distinguishing between two independent samples $\mathbf{G}_n^1,\mathbf{G}_n^2$ of a binomial random graph $G(n,p)$ by first order (FO) sentences. Shelah and Spencer proved that, for a constant $\alpha\in(0,1)$, $G(n,n^{-\alpha
Externí odkaz:
http://arxiv.org/abs/2405.09146