F. Clemen

activity

20182026

most citedRainbow Subgraphs in Edge-colored Complete Graphs -- Answering two Questions by Erdős and Tuza

13 citations · 49 across the 30 of their papers we have counts for

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31 papers · 1 filter

math.CO2026

On the number of regular simplices in odd dimensions

Felix Christian Clemen, Dingyuan Liu

Let $S_{d}^{k} (n)$ denote the maximum number of regular $(k - 1)$ -simplices spanned by $n$ points in $R^{d}$ . For all fixed $r \geq k \geq 3$ , the exact value of $S_{2 r}^{k} (n)$ was re…

math.CO2026

A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs

Natalie Behague, Felix Christian Clemen, Joseph Hyde +1

We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured $3$ -graph to contain a colour-biased tight Hamilton cycle. This confirms a conj…

math.CO2026

Triangle-Saturated Graphs in the Semi-Random Graph Process

Felix Christian Clemen, Pawel Pralat

The semi-random graph process is an adaptive random graph process in which an online algorithm is initially given an empty graph on $n$ vertices. In each round, a vertex $u$ is pre…

math.CO2026

Geometric Sidon Problems

Felix Christian Clemen, Jakob Führer, Oliver Roche-Newton

This paper considers geometric problems of the following type: given a point set $P \subset R^{2}$ , one seeks a large subset avoiding a prescribed geometric configuration. Ou…

math.CO2026

On Tournament Anti-Sidorenko Orientations of Trees

Hao Chen, Felix Christian Clemen, Jonathan A. Noel

An oriented graph $H$ is said to be tournament anti-Sidorenko if the homomorphism density of $H$ in any tournament $T$ is bounded above by the homomorphism densit…

math.CO2025

The number of regular simplices in higher dimensions

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

We study the extremal function $S_{d}^{k} (n)$ , defined as the maximum number of regular $(k - 1)$ -simplices spanned by $n$ points in $R^{d}$ . For any fixed $d \geq 2 k \geq 6$ , we dete…

math.CO2025

Maximizing Alternating Paths via Entropy

Hao Chen, Felix Christian Clemen, Jonathan A. Noel

We prove that if $G$ is an $n$ -vertex graph whose edges are coloured with red and blue, then the number of colour-alternating walks of length $2 k + 1$ with $k + 1$ red edges and $k$ bl…

math.CO2025

On multiplicities of interpoint distances

Felix Christian Clemen, Adrian Dumitrescu, Dingyuan Liu

Given a set $X \subseteq R^{2}$ of $n$ points and a distance $d > 0$ , the multiplicity of $d$ is the number of times the distance $d$ appears between points in $X$ . Let $a_1(X)…

math.CO2024

Subset selection problems in planar point sets

József Balogh, Felix Christian Clemen, Adrian Dumitrescu +1

Given a finite point set satisfying condition $A$ , the subset selection problem asks, how large of a subset satisfying condition $B$ can be extracted? In this p…

math.CO2024

Applications of Sparse Hypergraph Colorings

Felix Christian Clemen

Many problems in extremal combinatorics can be reduced to determining the independence number of a specific auxiliary hypergraph. We present two such problems, one from discrete ge…

math.CO2024

Crossing Numbers of Billiard Curves in the Multidimensional Box via Translation Surfaces

Felix Christian Clemen, Peter Kaiser

The billiard table is modeled as an $n$ -dimensional box $[0, a_{1}] \times [0, a_{2}] \times \dots \times [0, a_{n}] \subset R^{n}$ , with each side having real-valued lengths $a_{i}$ th…

math.CO2023

On a Traveling Salesman Problem for Points in the Unit Cube

József Balogh, Felix Christian Clemen, Adrian Dumitrescu

Let $X$ be an $n$ -element point set in the $k$ -dimensional unit cube $[0, 1]^{k}$ where $k \geq 2$ . According to an old result of Bollobás and Meir (1992), there exists a cycle (tour)…

math.CO2023

A note on balanced edge-colorings avoiding rainbow cliques of size four

Felix Christian Clemen, Adam Zsolt Wagner

A balanced edge-coloring of the complete graph is an edge-coloring such that every vertex is incident to each color the same number of times. In this short note, we present a const…

math.CO2023

Almost Congruent Triangles

József Balogh, Felix Christian Clemen, Adrian Dumitrescu

Almost $50$ years ago Erdős and Purdy asked the following question: Given $n$ points in the plane, how many triangles can be approximate congruent to equilateral triangles? They po…

math.CO2022

Online Ramsey numbers of ordered paths and cycles

Felix Christian Clemen, Emily Heath, Mikhail Lavrov

An ordered graph is a graph with a linear ordering on its vertices. The online Ramsey game for ordered graphs $G$ and $H$ is played on an infinite sequence of vertices; on each tur…

math.CO2022★ 13 cited

Rainbow Subgraphs in Edge-colored Complete Graphs -- Answering two Questions by Erdős and Tuza

Maria Axenovich, Felix Christian Clemen

An edge-coloring of a complete graph with a set of colors $C$ is called completely balanced if any vertex is incident to the same number of edges of each color from $C$ . Erdős and…

math.CO2022

Unavoidable order-size pairs in hypergraphs -- positive forcing density

Maria Axenovich, József Balogh, Felix Christian Clemen +1

Erdős, Füredi, Rothschild and Sós initiated a study of classes of graphs that forbid every induced subgraph on a given number $m$ of vertices and number $f$ of edges. Extending the…

math.CO2022★ 1 cited

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

József Balogh, Felix Christian Clemen, Haoran Luo

For every integer $t \geq 0$ , denote by $F_{5}^{t}$ the hypergraph on vertex set ${1, 2, \dots, 5 + t}$ with hyperedges ${123, 124} \cup {34 k : 5 \leq k \leq 5 + t}$ . We determine $\mathr…

math.CO2022★ 4 cited

The Spectrum of Triangle-free Graphs

József Balogh, Felix Christian Clemen, Bernard Lidický +2

Denote by $q_{n} (G)$ the smallest eigenvalue of the signless Laplacian matrix of an $n$ -vertex graph $G$ . Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \le…

math.CO2022

10 Problems for Partitions of Triangle-free Graphs

József Balogh, Felix Christian Clemen, Bernard Lidický

We will state 10 problems, and solve some of them, for partitions in triangle-free graphs related to Erdős' Sparse Half Conjecture. Among others we prove the following variant of i…

math.CO2021

Chasing the Threshold Bias of the 3-AP Game

Albert Cao, Felix Christian Clemen, Sean English +4

In a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure while Breaker wins if they prevent Maker from winning indefi…

math.CO2021★ 11 cited

Solving Turán's Tetrahedron Problem for the $ℓ_{2}$ -Norm

József Balogh, Felix Christian Clemen, Bernard Lidický

Turán's famous tetrahedron problem is to compute the Turán density of the tetrahedron $K_{4}^{3}$ . This is equivalent to determining the maximum $ℓ_{1}$ -norm of the codegree vector of…

math.CO2021★ 1 cited

Hypergraph Turán Problems in $ℓ_{2}$ -Norm

József Balogh, Felix Christian Clemen, Bernard Lidický

There are various different notions measuring extremality of hypergraphs. In this survey we compare the recently introduced notion of the codegree squared extremal function with th…

math.CO2021

Counting $r$ -graphs without forbidden configurations

József Balogh, Felix Christian Clemen, Letícia Mattos

One of the major problems in combinatorics is to determine the number of $r$ -uniform hypergraphs ( $r$ -graphs) on $n$ vertices which are free of certain forbidden structures. This p…

On the number of regular simplices in odd dimensions

A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs

Triangle-Saturated Graphs in the Semi-Random Graph Process

Geometric Sidon Problems

On Tournament Anti-Sidorenko Orientations of Trees

The number of regular simplices in higher dimensions

Maximizing Alternating Paths via Entropy

On multiplicities of interpoint distances

Subset selection problems in planar point sets

Applications of Sparse Hypergraph Colorings

Crossing Numbers of Billiard Curves in the Multidimensional Box via Translation Surfaces

On a Traveling Salesman Problem for Points in the Unit Cube

A note on balanced edge-colorings avoiding rainbow cliques of size four

Almost Congruent Triangles

Online Ramsey numbers of ordered paths and cycles

Rainbow Subgraphs in Edge-colored Complete Graphs -- Answering two Questions by Erdős and Tuza

Unavoidable order-size pairs in hypergraphs -- positive forcing density

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

The Spectrum of Triangle-free Graphs

10 Problems for Partitions of Triangle-free Graphs

Chasing the Threshold Bias of the 3-AP Game

Solving Turán's Tetrahedron Problem for the ℓ2​-Norm

Hypergraph Turán Problems in ℓ2​-Norm

Counting r-graphs without forbidden configurations

Solving Turán's Tetrahedron Problem for the $ℓ_{2}$ -Norm

Hypergraph Turán Problems in $ℓ_{2}$ -Norm

Counting $r$ -graphs without forbidden configurations