Asaf Ferber

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8 papers · 1 filter

math.CO2025

Sunflowers in set systems with small VC-dimension

JÃ³zsef Balogh, Anton Bernshteyn, Michelle Delcourt +2

A family of $r$ distinct sets ${A_{1}, \dots, A_{r}}$ is an $r$ -sunflower if for all $1 ⩽ i < j ⩽ r$ and $1 ⩽ i^{'} < j^{'} ⩽ r$ , we have $A_i \cap A_j = A_…

math.CO2025

On the edge expansion of random polytopes

Asaf Ferber, Michael Krivelevich, Marcelo Sales +1

A $0/1$ -polytope in $R^{n}$ is the convex hull of a subset of ${0, 1}^{n}$ . The graph of a polytope $P$ is the graph whose vertices are the zero-dimensional faces of $P$ and…

math.CO2025

Sharp Threshold for Cliques in Random 0/1 Polytope Graphs

Catherine Babecki, Tycho Elling, Asaf Ferber

We study graph-theoretic properties of random $0/1$ polytopes. Specifically, let $Q_{p}^{n} \subseteq {0, 1}^{n}$ be a random subset where each point is included independently with prob…

math.CO2025

Minimum degree edge-disjoint Hamilton cycles in random directed graphs

Asaf Ferber, Adva Mond

In this paper we consider the problem of finding ``as many edge-disjoint Hamilton cycles as possible'' in the binomial random digraph $D_{n, p}$ . We show that a typical $D_{n, p}$ co…

math.CO2024

Hamiltonicity of Sparse Pseudorandom Graphs

Asaf Ferber, Jie Han, Dingjia Mao +1

We show that every $(n, d, I^»)$ -graph contains a Hamilton cycle for sufficiently large $n$ , assuming that $d \geq lo g^{6} n$ and $I^» \leq c d$ , where $c = \frac{1}{70000}$ . This significa…

math.CO2024

Dirac-type Problem of Rainbow matchings and Hamilton cycles in Random Graphs

Asaf Ferber, Jie Han, Dingjia Mao

Given a family of graphs $G_{1}, \dots, G_{n}$ on the same vertex set $[n]$ , a rainbow Hamilton cycle is a Hamilton cycle on $[n]$ such that each $G_{c}$ contributes exactly one edge. We…