Zobrazeno 1 - 10
of 36 403
pro vyhledávání: '"hypercubes"'
Autor:
Bérczi, Gergely, Wagner, Adam Zsolt
We apply a generative AI pattern-recognition technique called PatternBoost to study bootstrap percolation on hypercubes. With this, we slightly improve the best existing upper bound for the size of percolating subsets of the hypercube.
Externí odkaz:
http://arxiv.org/abs/2411.19734
Autor:
Cobeli, Cristian, Zaharescu, Alexandru
For any odd prime $p$ and any integer $N\ge 0$, let $\mathcal{V}(p,N)$ be the set of vertices of the cyclotomic box $\mathscr{B} = \mathscr{B}(p,N)$ of edge size $2N$ and centered at the origin $O$ of the ring of integers $\mathbb{Z}[\omega]$ of the
Externí odkaz:
http://arxiv.org/abs/2410.14473
Autor:
Zheng, Michael
This paper is about the rainbow dual of the Hales Jewett number, providing general bounds an anti-Hales Jewett Number for hypercubes of length k and dimension n denoted $ah(k, n).$ The best general bounds this paper provides are: $(k-1)^n < ah(k, n)
Externí odkaz:
http://arxiv.org/abs/2410.12192
Autor:
Kandekar, S. A., Mane, S. A.
In 2013, Tapolcai demonstrated that a network with two completely independent spanning trees (CISTs) is sufficient for implementing protection routing. In a graph \( G \) with \( k \geq 2 \) spanning trees, denoted as \( T = \{T_1, T_2, \ldots, T_k\}
Externí odkaz:
http://arxiv.org/abs/2410.03379
Autor:
Ning, Wantao1 (AUTHOR) wtning@xidian.edu.cn, Li, Hao2 (AUTHOR) li@lri.fr
Publikováno v:
Axioms (2075-1680). Mar2024, Vol. 13 Issue 3, p194. 12p.
Autor:
MIKLAVIČ, ŠTEFKO1,2, ŠPARL, PRIMOŽ2,3,4 primoz.sparl@pef.uni-lj.si
Publikováno v:
Discussiones Mathematicae: Graph Theory. 2024, Vol. 44 Issue 1, p17-33. 17p.
Structure connectivity and substructure connectivity are innovative indicators for assessing network reliability and fault tolerance. Similarly, fault diameter evaluates fault tolerance and transmission delays in networks. This paper extends the conc
Externí odkaz:
http://arxiv.org/abs/2412.09885
Autor:
Axenovich, Maria, Liu, Dingyuan
A subset $M$ of vertices in a graph $G$ is a mutual-visibility set if for any two vertices $u,v\in{M}$ there exists a shortest $u$-$v$ path in $G$ that contains no elements of $M$ as internal vertices. Let $\chi_{\mu}(G)$ be the least number of color
Externí odkaz:
http://arxiv.org/abs/2411.12124
How small can a set of vertices in the $n$-dimensional hypercube $Q_n$ be if it meets every copy of $Q_d$? The asymptotic density of such a set (for $d$ fixed and $n$ large) is denoted by $\gamma_d$. It is easy to see that $\gamma_d \leq 1/(d+1)$, an
Externí odkaz:
http://arxiv.org/abs/2411.09445