M. Sales

activity

20202026

most citedOn quantitative aspects of a canonisation theorem for edge-orderings

5 citations · 5 across the 12 of their papers we have counts for

collaborators

14 papers

quant-ph2026

Asymptotic entanglement in circle stabilizer states and states forbidding arbitrary vertex-minors

Kenneth Goodenough, Marcelo Sales

Stabilizer states play a central role in quantum information theory, and understanding their entanglement has motivated a large body of work. A well-studied question in particular…

math.CO2026

Even smaller universal posets

József Balogh, Ramon I. Garcia, Marcelo Sales

We show that for every $η > 0$ and sufficiently large $n$ , there exists a poset of size $2^{(1 + η) n /2}$ containing all the $n$ -element posets as induced subposets. This improves a rec…

math.CO2022

The codegree Turán density of tight cycles minus one edge

Simón Piga, Marcelo Sales, Bjarne Schülke

Given $α > 0$ and an integer $ℓ \geq 5$ , we prove that every sufficiently large $3$ -uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $α n$ …

math.CO2022

On the Ramsey number of daisies II

Marcelo Sales

A $(k + r)$ -uniform hypergraph $H$ on $(k + m)$ vertices is an $(r, m, k)$ -daisy if there exists a partition of the vertices $V (H) = K \cup M$ with $∣ K ∣ = k$ , $∣ M ∣ = m$ such that the set of edg…

math.CO2022

On the Ramsey number of daisies I

Pavel Pudlák, Vojtěch Rödl, Marcelo Sales

Daisies are a special type of hypergraphs introduced by Bollobás, Leader and Malvenuto. An $r$ -daisy determined by a pair of disjoint sets $K$ and $M$ is the $(r + ∣ K ∣)$ -uniform hype…

math.CO2022

A local version of Katona's intersection theorem

Marcelo Sales, Bjarne Schülke

Katona's intersection theorem states that every intersecting family $F \subseteq [n]^{(k)}$ satisfies $∣ \partial F ∣ \geq ∣ F ∣$ , where $\partial…

math.CO2022

Some results and problems on clique coverings of hypergraphs

Vojtech Rödl, Marcelo Sales

For a $k$ -uniform hypergraph $F$ we consider the parameter $Θ (F)$ , the minimum size of a clique cover of the of $F$ . We derive bounds on $Θ (F)$ for $F$ belonging to various classes…

math.CO2022

Independence number of hypergraphs under degree conditions

Vojtěch Rödl, Marcelo Sales, Yi Zhao

A well-known result of Ajtai et al. from 1982 states that every $k$ -graph $H$ on $n$ vertices, with girth at least five, and average degree $t^{k - 1}$ contains an independent set of…

math.CO2021

A note on the induced Ramsey theorem for spaces

Bryce Frederickson, Vojtech Rödl, Marcelo Sales

The aim of this note is to give a simplified proof of the induced version of the Ramsey theorem for vector spaces first proved by H. J. Prömel.

math.CO2021

Every Steiner triple system contains an almost spanning d-ary hypertree

Andrii Arman, Vojtěch Rödl, Marcelo Tadeu Sales

In this paper we make a partial progress on the following conjecture: for every $μ > 0$ and large enough $n$ , every Steiner triple system $S$ on at least $(1 + μ) n$ vertices contains e…

math.CO2021

Independent sets in subgraphs of a shift graph

Andrii Arman, Vojtěch Rödl, Marcelo Tadeu Sales

Erdős, Hajnal and Szemerédi proved that any subset $G$ of vertices of a shift graph $Sh_{n}^{k}$ has the property that the independence number of the subgraph induced by $G$ …

math.CO2021

Colourful matchings

Andrii Arman, Vojtěch Rödl, Marcelo Tadeu Sales

Suppose a committee consisting of three members has to match $n$ candidates to $n$ different positions. Each member of the committee proposes a matching, however the proposed match…

math.CO2021

A blurred view of Van der Waerden type theorems

Vojtech Rödl, Marcelo Sales

Let $A P_{k} = {a, a + d, \dots, a + (k - 1) d}$ be an arithmetic progression. For $ε > 0$ we call a set $A P_{k} (ε) = {x_{0}, \dots, x_{k - 1}}$ an $ε$ -approximate arithmetic progression if for some $a…

math.CO2020★ 5 cited

On quantitative aspects of a canonisation theorem for edge-orderings

Christian Reiher, Vojtěch Rödl, Marcelo Sales +2

For integers $k \geq 2$ and $N \geq 2 k + 1$ there are $k! 2^{k}$ canonical orderings of the edges of the complete $k$ -uniform hypergraph with vertex set $[N] = {1, 2, \dots, N}$ . These are…