Christian Reiher

activity

20122026

most citedThe Clique Density Theorem

109 citations · 453 across the 60 of their papers we have counts for

collaborators

65 papers

math.QA2026

Higher Fomin-Kirillov algebras are infinite-dimensional

N. Andruskiewitsch, I. Angiono, I. Heckenberger +3

We show that the Fomin--Kirillov algebras $F K_{n}$ are infinite-dimensional for $n \geq 6$ . This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate t…

math.CO2026

Regularity method for hypergraphs with $4$ -cycle-free links

Ayush Basu, Christian Reiher, Vojtěch Rödl +1

We extend the hypergraph regularity method to sparse $3$ -uniform hypergraphs whose vertex links are $C_{4}$ -free. In other words, we consider hypergraphs $H = (V, E)$ that are $K_{1,2,2…

math.CO2026

Canonical Ramsey theorem for graphs with clean intersections

Matías Azócar Carvajal, Ayush Basu, Christian Reiher +3

Extending earlier results of Nešetřil and Rödl [Selective graphs and hypergraphs, Ann. Discrete Math. 3 (1978), 181--189], we show that for every ordered graph $F$ there exist an o…

math.CO2026

Linearly distributive coherence in the absence of units

Max Demirdilek, Christian Reiher, Christoph Schweigert

Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in pa…

math.CO2026

Large sum-free sets in finite vector spaces II

Christian Reiher, Sofia Zotova

Answering a question of Leo Versteegen, we prove that for $n \geq 3$ every sum-free set $A \subseteq F_{5}^{n}$ with $∣ A ∣ \geq 28 \cdot 5^{n - 3}$ is either contained in the union of t…

math.CO2026

The complete picture for clique factors in randomly perturbed graphs

Sylwia Antoniuk, Nina Kamčev, Christian Reiher +1

A randomly perturbed graph $G^{p} = G_{α} \cup G_{n, p}$ is obtained by taking a deterministic $n$ -vertex graph $G_{α} = (V, E)$ with minimum degree $δ (G) \geq α n$ and adding the edges of th…

math.CO2025

Unavoidable subgraphs in Ramsey graphs

Christian Reiher, Vojtěch Rödl, Mathias Schacht

We study subgraphs that appear in large Ramsey graphs for a given graph $F$ . The recent girth Ramsey theorem of the first two authors asserts that there are Ramsey graphs such that…

math.CO2025

Relative Turán densities of ordered graphs

Christian Reiher, Vojtěch Rödl, Marcelo Sales +1

We introduce a modification of the Turán density of ordered graphs and investigate this graph parameter.

math.CO2025

Minimum degree in simplicial complexes

Christian Reiher, Bjarne Schülke

Given $d \in N$ , let $α (d)$ be the largest real number such that every abstract simplicial complex $S$ with $0<\vert\mathcal{S}\vert\leqα(d)\vert V(\mathcal{S})\ve…

math.CO2024

Clique factors in randomly perturbed graphs: the transition points

Sylwia Antoniuk, Nina Kamčev, Christian Reiher

A randomly perturbed graph $G^{p} = G_{α} \cup G (n, p)$ is obtained by taking a deterministic $n$ -vertex graph $G_{α} = (V, E)$ with minimum degree $δ (G) \geq α n$ and adding the edges of the…

math.CO2024

Sets and partitions minimising small differences

Sylwia Antoniuk, Christian Reiher

For a bounded measurable set $A \subseteq R$ we denote the Lebesgue measure of ${(x, y) \in A^{2} : x \leq y \leq x + 1}$ by $Φ (A)$ . We prove that if $I=A_1\cup\dots\cup A_{k+…

math.CO2024

Ramsey-type problems for generalised Sidon sets

Christian Reiher, Vojtěch Rödl, Mathias Schacht

We establish the existence of generalised Sidon sets enjoying additional Ramsey-type properties, which are motivated by questions of Erdős and Newman and of Alon and Erdős.

math.CO2024

Large sum-free sets in finite vector spaces I

Christian Reiher, Sofia Zotova

Let $p$ be a prime number with $p \equiv 2 (mod 3)$ and let $n \geq 1$ be a dimension. It is known that a sum-free subset of $F_{p}^{n}$ can have at most the size $\frac13(p+1)p…

math.CO2024

On Lev's periodicity conjecture

Christian Reiher

We classify the sum-free subsets of $F_{3}^{n}$ whose density exceeds $\frac{1}{6}$ . This yields a resolution of Vsevolod Lev's periodicity conjecture, which asserts that if a su…

math.CO2024

Strong Brandt-Thomassé Theorems

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

Solving a long standing conjecture of Erdős and Simonovits, Brandt and Thomassé proved that the chromatic number of each triangle-free graph $G$ such that $δ (G) > ∣ V (G) ∣/3$ is at mos…

math.CO2024

Graphs of large girth

Christian Reiher

This survey on graphs of large girth consists of two parts. The first deals with some aspects of algebraic and extremal graph theory loosely related to the Moore bound. Our point o…

math.CO2024

Obligatory hypergraphs

Christian Reiher

Erdős and Hajnal proved that every graph of uncountable chromatic number contains arbitrarily large finite, complete, bipartite graphs. We extend this result to hypergraphs.

math.CO2023

Colouring versus density in integers and Hales-Jewett cubes

Christian Reiher, Vojtěch Rödl, Marcelo Sales

We construct for every integer $k \geq 3$ and every real $μ \in (0, \frac{k - 1}{k})$ a set of integers $X = X (k, μ)$ which, when coloured with finitely many colours, contains a monochrom…

math.CO2023

The girth Ramsey theorem

Christian Reiher, Vojtěch Rödl

Given a hypergraph $F$ and a number of colours $r$ , there exists a hypergraph $H$ of the same girth satisfying $H ⟶ (F)_{r}$ . Moreover, for every linear hypergraph $F$ t…

math.CO2023

Note on the Theorem of Balog, Szemerédi, and Gowers

Christian Reiher, Tomasz Schoen

We prove that every additive set $A$ with energy $E (A) \geq ∣ A ∣^{3} / K$ has a subset $A^{'} \subseteq A$ of size $∣ A^{'} ∣ \geq (1 - ε) K^{- 1/2} ∣ A ∣$ such that $|A'-A'|\le O_\varepsilon(K^{…

math.CO2023

The next case of Andrásfai's conjecture

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

Let $ex (n, s)$ denote the maximum number of edges in a triangle-free graph on $n$ vertices which contains no independent sets larger than $s$ . The behaviour of $\mathrm{ex}…

math.CO2022

Turán density of cliques of order five in $3$ -uniform hypergraphs with quasirandom links

Sören Berger, Simón Piga, Christian Reiher +2

We show that $3$ -uniform hypergraphs with the property that all vertices have a quasirandom link graph with density bigger than $1/3$ contain a clique on five vertices. This result…

math.CO2022

Two disjoint cycles in digraphs

Mikołaj Lewandowski, Joanna Polcyn, Christian Reiher

Bermond and Thomassen conjectured that every digraph with minimum outdegree at least $2 k - 1$ contains $k$ vertex disjoint cycles. So far the conjecture was verified for $k \leq 3$ . He…

math.CO2021★ 1 cited

K_4-free graphs have sparse halves

Christian Reiher

Every $K_{4}$ -free graph on $n$ vertices has a set of $⌊ n /2 ⌋$ vertices spanning at most $n^{2} /18$ edges.

Higher Fomin-Kirillov algebras are infinite-dimensional

Regularity method for hypergraphs with 4-cycle-free links

Canonical Ramsey theorem for graphs with clean intersections

Linearly distributive coherence in the absence of units

Large sum-free sets in finite vector spaces II

The complete picture for clique factors in randomly perturbed graphs

Unavoidable subgraphs in Ramsey graphs

Relative Turán densities of ordered graphs

Minimum degree in simplicial complexes

Clique factors in randomly perturbed graphs: the transition points

Sets and partitions minimising small differences

Ramsey-type problems for generalised Sidon sets

Large sum-free sets in finite vector spaces I

On Lev's periodicity conjecture

Strong Brandt-Thomassé Theorems

Graphs of large girth

Obligatory hypergraphs

Colouring versus density in integers and Hales-Jewett cubes

The girth Ramsey theorem

Note on the Theorem of Balog, Szemerédi, and Gowers

The next case of Andrásfai's conjecture

Turán density of cliques of order five in 3-uniform hypergraphs with quasirandom links

Two disjoint cycles in digraphs

K_4-free graphs have sparse halves

Regularity method for hypergraphs with $4$ -cycle-free links

Turán density of cliques of order five in $3$ -uniform hypergraphs with quasirandom links