A. Sgueglia

activity

20202026

most citedTriangles in randomly perturbed graphs

13 citations · 19 across the 14 of their papers we have counts for

collaborators

16 papers

math.CO2026

The perfect 1-factorisation conjecture holds asymptotically

Yangyang Cheng, Amedeo Sgueglia

A famous conjecture of Anton Kotzig states that for every even integer $n \geq 4$ , the complete graph $K_{n}$ of order $n$ can be decomposed into $n - 1$ perfect matchings such that ev…

math.CO2026

Ordered Ramsey and Turán numbers of alternating paths and their variants

Gaurav Kucheriya, Allan Lo, Jan Petr +2

An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph $K_{N}^{<}$ is the complete graph with vertex set $[N]$ equipped with the natura…

math.CO2025

On Kotzig's conjecture in random graphs

Stefan Glock, Amedeo Sgueglia

In 1963, Anton Kotzig famously conjectured that $K_{n}$ , the complete graph of order $n$ , where $n$ is even, can be decomposed into $n - 1$ perfect matchings such that every pair of…

math.CO2025

Steiner triple systems with high discrepancy

Lior Gishboliner, Stefan Glock, Amedeo Sgueglia

In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed $r \geq 3$ and $n \equiv 1, 3 (mod 6)$ , any $r$ -co…

math.CO2025

Defect and transference versions of the Alon-Frankl-Lovasz theorem

Lior Gishboliner, Stefan Glock, Peleg Michaeli +1

Confirming a conjecture of Erdős on the chromatic number of Kneser hypergraphs, Alon, Frankl and Lovász proved that in any $q$ -colouring of the edges of the complete $r$ -uniform hy…

math.CO2024

Dirac's theorem for graphs of bounded bandwidth

Alberto Espuny Díaz, Pranshu Gupta, Domenico Mergoni Cecchelli +2

We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph $K_{2, ℓ}$ . This…

math.CO2024

Spanning spheres in Dirac hypergraphs

Freddie Illingworth, Richard Lang, Alp Müyesser +2

We show that a $k$ -uniform hypergraph on $n$ vertices has a spanning subgraph homeomorphic to the $(k - 1)$ -dimensional sphere provided that $H$ has no isolated vertices and each s…

math.CO2023★ 3 cited

Tight Hamilton cycles with high discrepancy

Lior Gishboliner, Stefan Glock, Amedeo Sgueglia

In this paper, we study discrepancy questions for spanning subgraphs of $k$ -uniform hypergraphs. Our main result is that, for any integers $k \geq 3$ and $r \geq 2$ , any $r$ -colourin…

math.CO2023

On a problem of Brown, Erdős and Sós

Shoham Letzter, Amedeo Sgueglia

Let $f^{(r)} (n; s, k)$ be the maximum number of edges in an $n$ -vertex $r$ -uniform hypergraph not containing a subhypergraph with $k$ edges on at most $s$ vertices. Recently, Delcour…

math.CO2023

Rainbow subgraphs of uniformly coloured randomly perturbed graphs

Kyriakos Katsamaktsis, Shoham Letzter, Amedeo Sgueglia

For a given $δ \in (0, 1)$ , the randomly perturbed graph model is defined as the union of any $n$ -vertex graph $G_{0}$ with minimum degree $δ n$ and the binomial random graph $\mathbf{G…

math.CO2023★ 2 cited

Rainbow Hamiltonicity in uniformly coloured perturbed digraphs

Kyriakos Katsamaktsis, Shoham Letzter, Amedeo Sgueglia

We investigate the existence of a rainbow Hamilton cycle in a uniformly edge-coloured randomly perturbed digraph. We show that for every $δ \in (0, 1)$ there exists $C = C (δ) > 0$ su…

math.CO2022

A general approach to transversal versions of Dirac-type theorems

Pranshu Gupta, Fabian Hamann, Alp Müyesser +2

Given a collection of hypergraphs $H = (H_{1}, \dots, H_{m})$ with the same vertex set, an $m$ -edge graph $F \subset \cup_{i \in [m]} H_{i}$ is a transversal if there is a bijection $…

math.CO2022★ 1 cited

The square of a Hamilton cycle in randomly perturbed graphs

Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1

We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given $α \in (0, 1)$ , the union of any $n$ -vertex graph wit…

math.CO2022

Multistage Positional Games

Juri Barkey, Dennis Clemens, Fabian Hamann +2

We initiate the study of a new variant of the Maker-Breaker positional game, which we call multistage game. Given a hypergraph $H = (X, F)$ and a bias $b…

math.CO2021

Cycle factors in randomly perturbed graphs

Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1

We study the problem of finding pairwise vertex-disjoint copies of the $ℓ$ -vertex cycle $C_{ℓ}$ in the randomly perturbed graph model, which is the union of a deterministic $n$ …

math.CO2020★ 13 cited

Triangles in randomly perturbed graphs

Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1

We study the problem of finding pairwise vertex-disjoint triangles in the randomly perturbed graph model, which is the union of any $n$ -vertex graph $G$ satisfying a given minimum…