T. Traetta

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20182022

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9 papers · 1 filter

math.CO2022

On non-isomorphic biminimal pots realizing the cube

M. M. Ferrari, A. Pasotti, T. Traetta

In this paper, we disprove a conjecture recently proposed in [L. Almodovar et al., arXiv:2108.00035] on the non-existence of biminimal pots realizing the cube, namely pots with the…

math.CO2022

Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem

A. C. Burgess, P. Danziger, A. Pastine +1

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group $G$ . When $G$ is cyclic, these types of matrices have been widely used to build uniform…

math.CO2021

Vertex-regular $1$ -factorizations in infinite graphs

Simone Costa, Tommaso Traetta

The existence of $1$ -factorizations of an infinite complete equipartite graph $K_{m} [n]$ (with $m$ parts of size $n$ ) admitting a vertex-regular automorphism group $G$ is known only…

math.CO2021

Factorizing the Rado graph and infinite complete graphs

Simone Costa, Tommaso Traetta

Let $F = {F_{α} : α \in A}$ be a family of infinite graphs, together with $Λ$ . The Factorization Problem $F P (F, Λ)$ asks whether $F$ can be real…

math.CO2020

The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class

Simona Bonvicini, Marco Buratti, Martino Garonzi +2

Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems,…

math.CO2019

A reduction of the spectrum problem for odd sun systems and the prime case

Marco Buratti, Anita Pasotti, Tommaso Traetta

A $k$ -cycle with a pendant edge attached to each vertex is called a $k$ -sun. The existence problem for $k$ -sun decompositions of $K_{v}$ , with $k$ odd, has been solved only when $k=3…