T. Traetta

activity

20152026

most citedMerging Combinatorial Design and Optimization: the Oberwolfach Problem

7 citations · 26 across the 20 of their papers we have counts for

collaborators

25 papers

math.CO2026

A note on near alternating sign matrices with prescribed row and column weights

Tommaso Traetta

We study near alternating sign matrices with prescribed row and column weights. After recalling the basic definitions and the necessary conditions coming from the Gale--Ryser theor…

math.CO2026

Characterizing pyramidal Hadamard designs with the largest number of fixed points

Tommaso Traetta

A symmetric $(v, k, λ)$ -design is said to be $f$ -pyramidal, with $f < v - 1$ , under the action of a group $G$ if $G$ acts as an automorphism group fixing $f$ points and acting sharply tr…

math.CO2025

On circular external difference families

A. Burgess, F. Merola, T. Traetta

Circular external difference families (CEDFs) are a recently-introduced variation of external difference families (EDFs) with applications to non-malleable threshold schemes: a $(v…

math.CO2025★ 1 cited

The existence of pyramidal Steiner triple systems over abelian groups

Yanxun Chang, Tommaso Traetta, Junling Zhou

A Steiner triple system STS $(v)$ is called $f$ -pyramidal if it has an automorphism group fixing $f$ points and acting sharply transitively on the remaining $v - f$ points. In this pa…

math.CO2024

Towards a solution of Archdeacon's conjecture on integer Heffter arrays

Marco Antonio Pellegrini, Tommaso Traetta

In this paper, we make significant progress on a conjecture proposed by Dan Archdeacon on the existence of integer Heffter arrays $H (m, n; s, k)$ whenever the necessary conditions hol…

math.CO2024★ 1 cited

A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs

M. Abreu, J. B. Gauci, D. Mattiolo +4

A proper total colouring of a graph $G$ is called harmonious if it has the further property that when replacing each unordered pair of incident vertices and edges with their colour…

math.CO2023

A survey on constructive methods for the Oberwolfach problem and its variants

Andrea Burgess, Peter Danziger, Tommaso Traetta

The generalized Oberwolfach problem asks for a decomposition of a graph $G$ into specified 2-regular spanning subgraphs $F_{1}, \dots, F_{k}$ , called factors. The classic Oberwolfach p…

math.CO2023

On the minisymposium problem

Peter Danziger, Eric Mendelsohn, Brett Stevens +1

The generalized Oberwolfach problem asks for a factorization of the complete graph $K_{v}$ into prescribed $2$ -factors and at most a $1$ -factor. When all $2$ -factors are pairwise iso…

math.CO2023★ 1 cited

A constructive solution to the Oberwolfach Problem with a large cycle

Tommaso Traetta

For every $2$ -regular graph $F$ of order $v$ , the Oberwolfach problem $O P (F)$ asks whether there is a $2$ -factorization of $K_{v}$ ( $v$ odd) or $K_{v}$ minus a $1$ -factor ( $v$ even) in…

math.CO2023★ 4 cited

Constructing generalized Heffter arrays via near alternating sign matrices

Lorenzo Mella, Tommaso Traetta

Let $S$ be a subset of a group $G$ (not necessarily abelian) such that $S \cap - S$ is empty or contains only elements of order $2$ , and let $\mathbf{h}=(h_1,\ldots, h_m)\in \mathb…

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.CO2020★ 6 cited

On the Oberwolfach problem for single-flip $2$ -factors via graceful labelings

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

Let $F$ be a $2$ -regular graph of order $v$ . The Oberwolfach problem $O P (F)$ , posed in 1967 and still open, asks for a decomposition of $K_{v}$ into copies of $F$ . In this paper we s…

math.CO2019★ 1 cited

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.CO2019★ 7 cited

Merging Combinatorial Design and Optimization: the Oberwolfach Problem

Fabio Salassa, Gabriele Dragotto, Tommaso Traetta +2

The Oberwolfach Problem $O P (F)$ -- posed by Gerhard Ringel in 1967 -- is a paradigmatic Combinatorial Design problem asking whether the complete graph $K_{v}$ decomposes into edge-di…

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…

math.CO2015★ 5 cited

On the Hamilton-Waterloo Problem with odd orders

A. Burgess, P. Danziger, T. Traetta

Given non-negative integers $v, m, n, α, β$ , the Hamilton-Waterloo problem asks for a factorization of the complete graph $K_{v}$ into $α$ $C_{m}$ -factors and $β$ $C_{n}$ -factors. Clearl…

math.CO2015

On the existence of unparalleled even cycle systems

Peter Danziger, Eric Mendelsohn, Tommaso Traetta

A $2 t$ -cycle system of order $v$ is a set $C$ of cycles whose edges partition the edge-set of $K_{v} - I$ (i.e., the complete graph minus the $1$ -factor $I$ ). If $v\equiv 0 \…

math.CO2015

On the full automorphism group of a Hamiltonian cycle system of odd order

Marco Buratti, Graham J. Lovegrove, Tommaso Traetta

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or th…

A note on near alternating sign matrices with prescribed row and column weights

Characterizing pyramidal Hadamard designs with the largest number of fixed points

On circular external difference families

The existence of pyramidal Steiner triple systems over abelian groups

Towards a solution of Archdeacon's conjecture on integer Heffter arrays

A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs

A survey on constructive methods for the Oberwolfach problem and its variants

On the minisymposium problem

A constructive solution to the Oberwolfach Problem with a large cycle

Constructing generalized Heffter arrays via near alternating sign matrices

On non-isomorphic biminimal pots realizing the cube

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

Vertex-regular 1-factorizations in infinite graphs

Factorizing the Rado graph and infinite complete graphs

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

On the Oberwolfach problem for single-flip 2-factors via graceful labelings

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

Cyclic cycle systems of the complete multipartite graph

Merging Combinatorial Design and Optimization: the Oberwolfach Problem

The Hamilton-Waterloo Problem with even cycle lengths

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

On the Hamilton-Waterloo Problem with odd orders

On the existence of unparalleled even cycle systems

On the full automorphism group of a Hamiltonian cycle system of odd order

Vertex-regular $1$ -factorizations in infinite graphs

On the Oberwolfach problem for single-flip $2$ -factors via graceful labelings