Zobrazeno 1 - 10
of 188
pro vyhledávání: '"Hefetz, Dan"'
Autor:
Hefetz, Dan, Krivelevich, Michael
Given positive integers $k \leq m$ and a graph $G$, a family of lists $L = \{L(v) : v \in V(G)\}$ is said to be a random $(k,m)$-list-assignment if for every $v \in V(G)$ the list $L(v)$ is a subset of $\{1, \ldots, m\}$ of size $k$, chosen uniformly
Externí odkaz:
http://arxiv.org/abs/2402.09998
Let $\tilde K_t$ denote the $3$-uniform linear clique of order $t$. Given an even integer $t \geq 4$, let $M$ denote the asymmetric maximal density of $\tilde K_t$ and $\tilde K_{t/2}$. We prove that there exists a constant $C>0$ such that, if $(H_n)
Externí odkaz:
http://arxiv.org/abs/2311.01750
The {\em discrepancy} of a matrix $M \in \mathbb{R}^{d \times n}$ is given by $\mathrm{DISC}(M) := \min_{\boldsymbol{x} \in \{-1,1\}^n} \|M\boldsymbol{x}\|_\infty$. An outstanding conjecture, attributed to Koml\'os, stipulates that $\mathrm{DISC}(M)
Externí odkaz:
http://arxiv.org/abs/2307.06285
Extremal properties of sparse graphs, randomly perturbed by the binomial random graph are considered. It is known that every $n$-vertex graph $G$ contains a complete minor of order $\Omega(n/\alpha(G))$. We prove that adding $\xi n$ random edges, whe
Externí odkaz:
http://arxiv.org/abs/2212.07192
Let $G$ be an $n$-vertex graph, where $\delta(G) \geq \delta n$ for some $\delta := \delta(n)$. A result of Bohman, Frieze and Martin from 2003 asserts that if $\alpha(G) = O \left(\delta^2 n \right)$, then perturbing $G$ via the addition of $\omega
Externí odkaz:
http://arxiv.org/abs/2206.12210
We obtain sufficient conditions for the emergence of spanning and almost-spanning bounded-degree {\sl rainbow} trees in various host graphs, having their edges coloured independently and uniformly at random, using a predetermined palette. Our first r
Externí odkaz:
http://arxiv.org/abs/2105.08315
Autor:
Gilboa, Shoni, Hefetz, Dan
Publikováno v:
Journal of Combinatorics, Vol. 14, No. 2 (2023), pp. 167-196
Semi-random processes involve an adaptive decision-maker, whose goal is to achieve some pre-determined objective in an online randomized environment. We introduce and study a semi-random multigraph process, which forms a no-replacement variant of the
Externí odkaz:
http://arxiv.org/abs/2009.07589
For two graphs $G$ and $H$, write $G \stackrel{\mathrm{rbw}}{\longrightarrow} H$ if $G$ has the property that every \emph{proper} colouring of its edges yields a \emph{rainbow} copy of $H$. We study the thresholds for such so-called \emph{anti-Ramsey
Externí odkaz:
http://arxiv.org/abs/2006.00588
Autor:
Aigner-Horev, Elad, Hefetz, Dan
Given an $n$-vertex graph $G$ with minimum degree at least $d n$ for some fixed $d > 0$, the distribution $G \cup \mathbb{G}(n,p)$ over the supergraphs of $G$ is referred to as a (random) {\sl perturbation} of $G$. We consider the distribution of edg
Externí odkaz:
http://arxiv.org/abs/2004.08637