R. Steiner

activity

20142023

most citedUniform bounds on sup-norms of holomorphic forms of real weight

7 citations · 44 across the 35 of their papers we have counts for

collaborators

Showing 2023Show all

9 papers · 1 filter

math.CO2023

Clustered Colouring of Odd- $H$ -Minor-Free Graphs

Robert Hickingbotham, Dong Yeap Kang, Sang-il Oum +2

The clustered chromatic number of a graph class $G$ is the minimum integer $c$ such that every graph $G \in G$ has a $c$ -colouring where each monochromatic compon…

math.CO2023

Finding dense minors using average degree

Kevin Hendrey, Sergey Norin, Raphael Steiner +1

Motivated by Hadwiger's conjecture, we study the problem of finding the densest possible $t$ -vertex minor in graphs of average degree at least $t - 1$ . We show that if $G$ has averag…

math.CO2023

Size-Ramsey numbers of structurally sparse graphs

Nemanja Draganić, Marc Kaufmann, David Munhá Correia +2

Size-Ramsey numbers are a central notion in combinatorics and have been widely studied since their introduction by Erdős, Faudree, Rousseau and Schelp in 1978. Research has mainly…

math.CO2023

A logarithmic bound for simultaneous embeddings of planar graphs

Raphael Steiner

A set $G$ of planar graphs on the same number $n$ of vertices is called simultaneously embeddable if there exists a set $P$ of $n$ points in the plane such that every gra…

math.CO2023

Chromatic number is not tournament-local

António Girão, Kevin Hendrey, Freddie Illingworth +4

Scott and Seymour conjectured the existence of a function $f : N \to N$ such that, for every graph $G$ and tournament $T$ on the same vertex set, $χ(G) \geqs…

math.CO2023

On Connectivity in Random Graph Models with Limited Dependencies

Johannes Lengler, Anders Martinsson, Kalina Petrova +4

For any positive edge density $p$ , a random graph in the Erdős-Renyi $G_{n, p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider r…

math.CO2023

On the choosability of $H$ -minor-free graphs

Olivier Fischer, Raphael Steiner

Given a graph $H$ , let us denote by $f_{χ} (H)$ and $f_{ℓ} (H)$ , respectively, the maximum chromatic number and the maximum list chromatic number of $H$ -minor-free graphs. Hadwiger's…

cs.CG2023

Linear Size Universal Point Sets for Classes of Planar Graphs

Stefan Felsner, Hendrik Schrezenmaier, Felix Schröder +1

A finite set $P$ of points in the plane is $n$ -universal with respect to a class $C$ of planar graphs if every $n$ -vertex graph in $C$ admits a crossing-free st…

math.NT2023

Sums of Cusp Form Coefficients Along Quadratic Sequences

Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1

Let $f (z) = \sum A (n) n^{(k - 1) /2} e (n z)$ be a cusp form of weight $k \geq 3$ on $Γ_{0} (N)$ with character $χ$ . By studying a certain shifted convolution sum, we prove that $\sum_{n \…

Clustered Colouring of Odd-H-Minor-Free Graphs

Finding dense minors using average degree

Size-Ramsey numbers of structurally sparse graphs

A logarithmic bound for simultaneous embeddings of planar graphs

Chromatic number is not tournament-local

On Connectivity in Random Graph Models with Limited Dependencies

On the choosability of H-minor-free graphs

Linear Size Universal Point Sets for Classes of Planar Graphs

Sums of Cusp Form Coefficients Along Quadratic Sequences

Clustered Colouring of Odd- $H$ -Minor-Free Graphs

On the choosability of $H$ -minor-free graphs