Benjamin Bedert

activity

20202026

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5 papers · 1 filter

math.CO2026

The Lovász conjecture holds for moderately dense Cayley graphs

Benjamin Bedert, Nemanja Draganić, Alp Müyesser +1

We show that there is an absolute constant $c > 0$ such that every large connected $n$ -vertex Cayley graph with degree $d \geq n^{1 - c}$ has a Hamilton cycle. This makes progress towar…

math.CO2025

Riesz products and the Lonely Runner Conjecture: A wider gap of loneliness

Benjamin Bedert

The lonely runner conjecture of Wills and Cusick asserts that if $n$ runners with distinct constant speeds run around a a circular unit length track, starting at a common time and…

math.CO2025

On Graham's rearrangement conjecture over $F_{2}^{n}$

Benjamin Bedert, Matija Bucić, Noah Kravitz +2

A sequence $s_{1}, s_{2}, \dots, s_{k}$ of elements of a group $G$ is called a valid ordering if the partial products $s_{1}, s_{1} s_{2}, \dots, s_{1} \dots s_{k}$ are all distinct. A long-standi…

math.CO2024

Graham's rearrangement conjecture beyond the rectification barrier

Benjamin Bedert, Noah Kravitz

A 1971 conjecture of Graham (later repeated by Erdős and Graham) asserts that every set $A \subseteq F_{p} ∖ {0}$ has an ordering whose partial sums are all distin…

math.CO2023

On unique sums in Abelian groups

Benjamin Bedert

Let $A$ be a subset of the cyclic group $Z / p Z$ with $p$ prime. It is a well-studied problem to determine how small $∣ A ∣$ can be if there is no unique sum in $A + A$ …

The Lovász conjecture holds for moderately dense Cayley graphs

Riesz products and the Lonely Runner Conjecture: A wider gap of loneliness

On Graham's rearrangement conjecture over F2n​

Graham's rearrangement conjecture beyond the rectification barrier

On unique sums in Abelian groups

On Graham's rearrangement conjecture over $F_{2}^{n}$