Vojtech Dvorák

activity

20192021

collaborators

6 papers

math.CO2021

A New Upper Bound for the Ramsey Number of Fans

Vojtěch Dvořák, Harry Metrebian

A fan $F_{n}$ is a graph consisting of $n$ triangles, all having precisely one common vertex. Currently, the best known bounds for the Ramsey number $R (F_{n})$ are $9n/2-5 \leq R(F_n)…

math.CO2021

The Maker-Breaker percolation game on the square lattice

Vojtěch Dvořák, Adva Mond, Victor Souza

We study the $(m, b)$ Maker-Breaker percolation game on $Z^{2}$ , introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the…

math.CO2020

Radius, Girth and Minimum Degree

Vojtěch Dvořák, Peter van Hintum, Amy Shaw +1

Given a connected graph $G$ on $n$ vertices, with minimum degree $δ \geq 2$ and girth at least $g \geq 4$ , what is the maximum radius $r$ this graph can have? Erdős, Pach, Pollack a…

math.CO2020

Improved Bound for Tomaszewski's Problem

Vojtěch Dvořák, Peter van Hintum, Marius Tiba

In 1986, Tomaszewski made the following conjecture. Given $n$ real numbers $a_{1}, ..., a_{n}$ with $\sum_{i = 1}^{n} a_{i}^{2} = 1$ , then of the $2^{n}$ signed sums $\pm a_{1} \pm ... \p…

math.CO2020

The Eternal Game Chromatic Number of Random Graphs

Vojtěch Dvořák, Rebekah Herrman, Peter van Hintum

The eternal graph colouring problem, recently introduced by Klostermeyer and Mendoza, is a version of the graph colouring game, where two players take turns properly colouring a gr…

math.CO2019

A Note on Norine's Antipodal-Colouring Conjecture

Vojtěch Dvořák

Norine's antipodal-colouring conjecture, in a form given by Feder and Subi, asserts that whenever the edges of the discrete cube are 2-coloured there must exist a path between two…