T. Traetta

activity

20182021

collaborators

6 papers

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…

math.CO2019

Cyclic cycle systems of the complete multipartite graph

Andrea Burgess, Francesca Merola, Tommaso Traetta

In this paper, we study the existence problem for cyclic $ℓ$ -cycle decompositions of the graph $K_{m} [n]$ , the complete multipartite graph with $m$ parts of size $n$ , and give nec…

math.CO2018

The Hamilton-Waterloo Problem with even cycle lengths

A. C. Burgess, P. Danziger, T. Traetta

The Hamilton-Waterloo Problem HWP $(v; m, n; α, β)$ asks for a 2-factorization of the complete graph $K_{v}$ or $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, into $α$ …

math.CO2018

On the Hamilton-Waterloo Problem with cycle lengths of distinct parities

Andrea Burgess, Peter Danziger, Tommaso Traetta

Let $K_{v}^{*}$ denote the complete graph $K_{v}$ if $v$ is odd and $K_{v} - I$ , the complete graph with the edges of a 1-factor removed, if $v$ is even. Given non-negative integers $v, M, N…