M. Sales

activity

20202026

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Showing 2021 · math.COShow all

5 papers · 2 filters

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…