A. Sgueglia

collaborators

8 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 TurÃ¡n 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.CO2026

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

Lior Gishboliner, Stefan Glock, Peleg Michaeli +1

Confirming a conjecture of ErdÅs on the chromatic number of Kneser hypergraphs, Alon, Frankl and LovÃ¡sz proved that in any $q$ -colouring of the edges of the complete $r$ -uniform…

math.CO2025

Rainbow subgraphs of uniformly coloured randomly perturbed graphs

Kyriakos Katsamaktsis, Shoham Letzter, Amedeo Sgueglia

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

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…