Persona

## TRAETTA Tommaso

Docenti di ruolo di IIa fascia

## Curriculum Vitae

2010. PhD (Dottorato) in Mathematics and Computer Science for the processing and representation of information and knowledge, Università degli Studi di Perugia, Italy

2006. MSc (Laurea Magistrale) in Mathematics “cum laude”, Università del Salento, Italy

2004. BSc (Laurea Triennale) in Mathematics “cum laude”, Università del Salento, Italy

Current Position

01.12.2021–present. Associate Professor – University of Brescia, Italy

Previous Positions

07.07-07.09.2022. Visiting Professor at Toronto Metropolitan University (ex Ryerson University), Toronto, Canada

08.12.2021-10.01.2022. Visiting Professor at Toronto Metropolitan University (ex Ryerson University), Toronto, Canada

01.12.2018–30.11.2021. Tenure Track Researcher (RTDB) – University of Brescia, Italy

16.04.2018–30.11.2018. Researcher (RTDA) – University of Padova, Italy

01.12.2017–31.03.2018. Post-doctoral Research Fellow – Ryerson University, Toronto (ON) Canada

01.12.2015–30.11.2017. Marie-Curie Fellow (INdAM-Cofund) – Ryerson University, Toronto (ON) Canada & Università degli Studi di Perugia, Italy

01.10.2015–30.11.2015. Post-doctoral Research Fellow (INDAM) – Ryerson University, Toronto (ON) Canada

01.09.2014–31.08.2015. Post-doctoral Research Fellow – Ryerson University, Toronto (ON) Canada

01.09.2013–31.08.2014. Post-doctoral Research Fellow – Università degli Studi di Perugia, Italy

01.11.2010–31.10.2012. Post-doctoral Research Fellow – Sapienza, University of Rome

2008–2009. Visiting Scientist – McMaster University, Hamilton (ON) Canada. Supervisor Prof. Alex Rosa

Habilitations and Awards

- Kirkman Medal 2013 - for outstanding contributions to combinatorics and its applications - by the Institute of Combinatorics and its Applications

Conference/Session Organization

18–24.06.2023. Minisymposium on “Combinatorial Designs and their Applications” at the 10th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia

01–02.02.2018. “Discretaly – A workshop in Discrete Mathematics”, Sapienza University of Rome, Italy

12–15.06.2017. Two minisymposia “In honour of the work of Alex Rosa” at “CanaDAM 2017”, Ryerson University, Toronto (ON) Canada

Editorial Work

2019–2021. Managing Editor of Ars Combinatoria

Research Projects and Associations

2019, 2023. Holder of funds for international research activities (“Fondi per attività a carattere internazionale 2019\_INTER\_DICATAM\_TRAETTA”) financed by the Ministry of University and Research

2020. Reviewer of a proposal for Post-Doc projects at University of Verona

2016–present. Member of the “Institute for Combinatorics and its Applications (ICA)”

2010–12. Project PRIN 2008, Disegni, grafi e i loro codici e gruppi (Designs, graphs and related codes and groups) - Coordinator: Prof. M. Gionfriddo

2009–present. Member of “Unione Matematica Italiana UMI (Italian Mathematical Union)”

2009–12,2014–present. Member of “Istituto Nazionale di Alta Matematica INDAM (Italian National Board for Higher Mathematics) - Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA)”

Research Interests

Combinatorial design theory, (infinite) Graph decompositions, Difference Families, Regular Steiner triple systems, Automorphisms of combinatorial structures, Graph factorizations, packings and coverings, Graph labelings, and applications to DNA self-assembly, Heffter arrays and Graph embeddings, Combinatorial matrices

Research Impact

Papers published/accepted in refereed journals: 33

Papers submitted for publication in refereed journals: 1

Preprint: 5

Total citations: 238 (Scopus)

H-index: 10 (Scopus)

Publications

Papers Published in Refereed Journals

1. T. Traetta. Some new results on 1-rotational 2-factorizations of the complete graph. Journal of Combinatorial Designs 18(2010), 237-247

2. G. Rinaldi, T. Traetta. Graph products and new solutions to Oberwolfach problems. Electronic Journal of Combinatorics 18(2011), P52

3. S. Bonvicini, M. Buratti, G. Rinaldi, T. Traetta. Some progress on the existence of 1-rotational Steiner Triple Systems. Designs, Codes and Cryptography 62(2012), 63-78

4. M. Buratti, T. Traetta. 2-starters, graceful labelings and a doubling construction for the Oberwolfach problem. Journal of Combinatorial Designs 20(2012), 483-503

5. T. Traetta, On a class of highly symmetric k-factorizations. Electronic Journal of Combinatorics 20(2013), P24

6. T. Traetta. A complete solution to the two-table Oberwolfach problems. Journal of Combinatorial Theory A 120(2013), 984-997

7. M. Buratti, G. Rinaldi, T. Traetta. Some results on 1-rotational Hamiltonian cycle systems. Journal of Combinatorial Designs 22(2014), 231–251

8. M. Buratti, S. Capparelli, F. Merola, G. Rinaldi, T. Traetta. A collection of results on Hamiltonian cycle systems with a nice automorphism group. Electronic Notes in Discrete Mathematics 40(2013), 245–252

9. R.A. Bailey, M. Buratti, G. Rinaldi, T. Traetta. On 2-pyramidal Hamiltonian cycle systems. Bulletin of the Belgian Mathematical Society—Simon Stevin 21(2014), 747-758

10. M. Buratti, T. Traetta. The structure of 2-pyramidal 2-factorizations. Graphs and Combinatorics 31(2015), 523-53

11. M. Buratti, G.J. Lovegrove, T. Traetta. On the full automorphism group of a Hamiltonian cycle system of odd order. Graphs and Combinatorics 31(2015), 1855-1865

12. F. Merola, T. Traetta. Infinitely many cyclic solutions to the Hamilton–Waterloo problem with odd length cycles. Discrete Mathematics 339(2016), 2267-2283

13. P. Danziger, E. Mendelsohn, T. Traetta. On the existence of unparalleled even cycle systems. European Journal of Combinatorics 59(2017), 11-22

14. M. Buratti, G. Rinaldi, T. Traetta. 3-pyramidal Steiner triple systems. Ars Mathematica Contemporanea 13(2017), 95-106

15. M. Buratti, H. Cao, D. Dai, T. Traetta. A complete solution to the existence of (k,\lambda)-cycle frames of type g^u. Journal of Combinatorial Designs 25(2017), 197–230

16. A.C. Burgess, P. Danziger, T. Traetta. On the Hamilton-Waterloo Problem with odd orders. Journal of Combinatorial Designs 25 (2017), 258–287

17. A.C. Burgess, P. Danziger, T. Traetta. On the Hamilton-Waterloo problem with odd cycle lengths. Journal of Combinatorial Designs 26 (2018), 51–83

18. A.C. Burgess, P. Danziger, T. Traetta. On the Hamilton-Waterloo Problem with cycle lengths of distinct parities. Discrete Mathematics 341 (2018), 1636-1644

19. A.C. Burgess, P. Danziger, T. Traetta. The Hamilton-Waterloo Problem with even cycle lengths. Discrete Mathematics, 342 (2019), 2213–2222

20. A.C. Burgess, P. Danziger, T. Traetta. On the generalized Oberwolfach Problem. Ars Mathematica Contemporanea 17(2019), 67–78

21. A.C. Burgess, F. Merola, T. Traetta. Cyclic cycle systems of the complete multipartite graph. Journal of Combinatorial Designs, 28(2020), 224–260

22. M. Buratti, A. Pasotti, T. Traetta. A reduction of the spectrum problem for odd sun systems and the prime case. Journal of Combinatorial Designs 29(2021), 5–37

23. F. Salassa, G. Dragotto, T. Traetta, M. Buratti, F. Della Croce. Merging combinatorial design and optimization: The Oberwolfach problem. Australasian Journal of Combinatorics 79 (2021), 141–166

24. S. Bonvicini, M. Buratti, M. Garonzi, G. Rinaldi, T. Traetta. The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class. Designs, Codes and Cryptography 89 (2021), 2725–2757

25. S. Costa, T. Traetta. Vertex-regular 1-factorizations in infinite graphs. Journal of Combinatorial Designs 30 (2022), 354-363

26. A.C. Burgess, P. Danziger, T. Traetta. On the Oberwolfach problem for single-flip 2-factors via graceful labelings. Journal of Combinatorial Theory A 189 (2022), 105–611

27. S. Costa, T. Traetta. Factorizing the Rado graph and infinite complete graphs, Ars Math. Contemp. (2023), doi:10.26493/1855-3974.2616.4a9

28. M. M. Ferrari, A. Pasotti, T. Traetta. On non-isomorphic biminimal pots realizing the cube, Bulletin of the ICA 98 (2023), 122-139

29. A. Burgess, P. Danziger, A. Pastine, T. Traetta. Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem, Journal of Combinatorial Theory A 201 (2024), 105803

30. L. Mella, T. Traetta. Constructing generalized Heffter arrays via near alternating sign matrices, accepted for publication in Journal of Combinatorial Theory A 205 (2024), 105873

31. P. Danziger, E. Mendelsohn, B. Stevens, T. Traetta, On the mini-symposium problem, accepted for publication in Ars Math. Contemp. (2023), doi:10.26493/1855-3974.2835.8f0

32. A. Burgess, P. Danziger, T. Traetta. A survey on constructive resolution methods for the Oberwolfach problem and its variants, Conference proceedings: New Advances in Designs, Codes and Cryptography Stinson66, (Toronto, Canada, June 13-17, 2022), Fields Institute Communications

33. T. Traetta. A constructive solution to the Oberwolfach problem with a large cycle, accepted for publication in Discrete Mathematics

Papers Submitted for Publication in Refereed Journals

34. M. Abreu, J. B. Gauci, D. Mattiolo, G. Mazzuoccolo, F. Romaniello, C. Rubio-Montiel, T. Traetta. A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs

Conference Presentations

Presentations as Plenary or Invited Speaker

02-04.02.2023. Invited speaker at the “International Conference on Recent Advances in Graph Theory and Allied Areas” (ICRAGAA23), Department of Mathematics, St. Aloysius College, Elthuruth, Thrissur, India. Talk title: Open problems in Graph Decompositions and new methods to approach them

13–14.09.2018. Plenary speaker at the workshop “Algebraic Graph Theory and Complex Networks - WAGTCN 2018”. University of Naples Federico II, Italy. Talk title: Parallel Classes in Cycle Decompositions

09–11.08.2018. Plenary speaker at the “Kliakhandler Conference - Graph Decompositions”. Michigan Technological University, Houghton, MI, USA. Talk title: Recent advances on 2-factorizations

05–09.03.2018. Plenary speaker at the Forty-Ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing (2018). Florida Atlantic University, Boca Raton, FL, USA. Talk title: The golden jubilee of the Oberwolfach problem

10–16.09.2017. Invited speaker at “Finite Geometries 2017 – 5th Irsee Conference”. Irsee, Germany. Talk title: On f-pyramidal Steiner triple systems

19–25.06.2011. Invited speaker at “Finite Geometries 2011 - 3rd Irsee Conference”. Irsee, Germany. Talk title: Open problems on regular and 1-rotational Steiner triple systems

Presentations as invited speaker at Minisymposia - Conference Sessions

02-05.06.2023. Invited speaker at the minisymposium on “Design Theory and Graph Decompositions” at the 2023 Canadian Mathematical Society Summer Meeting, Ottawa (ON), Canada. Talk title: Generalized Heffter arrays and near alternating sign matrices

20–26.06.2021. Invited speaker at the special session on Combinatorial Designs within the “8th European Congress of Mathematics (8ECM)”. Talk title: On the Oberwolfach Problem for single-flip 2-factors via graceful labelings

07–11.06.2021. Invited speaker at the special session on Graph Decompositions within the “CMS 75th+1 Anniversary Summer Meeting, Ottawa”. Talk title: Highly symmetric Kirkman triple systems

08–11.12.2017. Invited speaker at the special session on Design Theory within the “2017 CMS Winter Meeting”. Waterloo (ON) Canada. Talk title: Steiner triple systems with well-behaved automorphisms

06–09.01.2016. Invited speaker at “AMS Special Session on Combinatorial Design Theory” within the “2016 Joint Mathematics Meetings”. Seattle, WA, USA. Talk title: Cycle decompositions: resolvable or without parallel classes

07–12.09.2015. Invited speaker at a special session of “XX Congresso dell’Unione Matematica Italiana”. Siena, Italia. Talk title: Resolvability vs. absence of parallel classes

05–08.06.2015. Invited speaker at the special session on “Graphs, Designs and Hypergraphs” within the “2015 Canadian Mathematical Society Summer Meeting”. Charlottetown (PEI) Canada. Talk title: On the Hamilton-Waterloo problem for a class of Cayley graphs

Contributed Conference Presentations:

18–24.06.2023. Minisymposium on “Combinatorial Designs and their Applications” at the 10th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia. Talk title: Row-sum matrices over abelian and generalized dihedral groups

14-19.05.2023. Invited participant at the workshop “Extremal Graphs arising from Designs and Configurations” held at the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Alberta, Canada.

21-23.10.2022. 34th Midwestern Conference on Combinatorics and Combinatorial Computing (MCCCC34), Illinois State University (Normal, IL, USA). Talk title: A constructive solution to the Oberwolfach problem with a large cycle.

26-30.06.2022. Combinatorial Constructions Workshop, University of Zagreb Faculty of Science, Croatia. Talk title: Row-sum matrices.

30.05-03.06.2022. Combinatorics 2022, Mantova, Italy. Talk title: Infinite graph factorizations.

03.09.2019. XXI Congresso dell’Unione Matematica Italiana, Pavia, Italy. Talk title: Open problems on Steiner triple systems

23–29.06.2019. 9th Slovenian International Conference on Graph Theory, Bled, Slovenia. Talk title: Pyramidal Steiner and Kirkman triple systems

03–09.06.2018. Combinatorics 2018, Arco, Italy. Talk title: Factorizations with subsystem

21–24.06.2017. HyGraDe, Sant'Alessio Siculo, Italy. Talk title: On a generalization of complete mappings

12-15.06.2017. CanaDAM 2017, Toronto, Canada. Talk title: Reverse 2-factorizations via graceful labelings

25.05.2017. 9th Shanghai Conference on Combinatorics, Shanghai, China. Talk title: Recent advances on $2$-factorizations of the complete graph

06-10.03.2017. 48th Southeastern International Conference on Combinatorics, Graph Theory & Computing, USA. Talk title: On f-pyramidal Steiner Triple Systems

13-16.02.2017. 2017 Coast Combinatorics Conference (26th), Kailua-Kona, HI, USA. Talk title: On f-pyramidal Steiner Triple Systems

13–17.06.2016. 3rd Istanbul Design Theory, Graph Theory and Combinatorics Workshop, Turkey. Talk title: Even Cycle Systems Without Parallel Classes

29.05–04.06.2016. Combinatorics 2016, Maratea, Italy. Talk title: A complete solution to the existence of (k, λ)-cycle frames of type g^u

17–19.09.2015. Giornate di Geometria 2015, Caserta, Italy. Talk title: Resolvability vs. absence of parallel classes

21–27.06.2015. 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia. Talk title: On the Hamilton-Waterloo problem for a class of Cayley graphs

21–24.05.2015. Discrete Math Days and Ontario Combinatorics Workshop, Ottawa, Canada. Talk title: On the Hamilton-Waterloo problem for a class of Cayley graphs

16–19.06.2014. SIAM Conference on Discrete Mathematics, Minneapolis, USA. Talk title: Cycle decompositions with a certain degree of symmetry

01–06.06.2014. Combinatorics 2014, Gaeta, Italy. Talk title: On the full automorphism group of a Hamiltonian cycle system

17–21.05.2014. Japan Conference on Graph Theory and Combinatorics, Tokyo, Japan. Talk title: New results on 1-rotational Hamiltonian cycle systems

09–15.09.2012. Combinatorics 2012, Perugia, Italy. Talk title: A complete solution to the two-table Oberwolfach problem

13–14.02.2012. Giornate di Geometria, Vicenza, Italy. Talk title: A step forward in the complete solution of the two-table Oberwolfach problem

25.06–01.07.2011. 2nd Istanbul Design Theory, Graph Theory and Combinatorics Conference, Istanbul, Turkey. Talk title: 2-starters, graceful labelings and a doubling construction for the Oberwolfach problem

23–28.05.2011. Seventh Shanghai Conference on Combinatorics, Shanghai, China. Talk title: On k-factorizations of the complete graph

04.03.2011. Giornata di Geometria, Vicenza, Italy. Talk title: Sistemi di terne di Steiner 1-rotazionali

27.06–03.07.2010. Combinatorics 2010, Verbania, Italy. Talk title: New infinite solutions to the Oberwolfach Problem

22–28.06.2008. Combinatorics 2008, Costermano, Italy. Talk title: Some new results on 1-rotational 2-factorizations of the complete graph

Seminar Presentations:

19.10.2018. “Discrete Mathematics Seminars”, Department of Computer Science, University of Verona, Italy. Talk title: Differences of Bijections and Applications

07.04.2017. “Seminario di Combinatoria”, University of Modena e Reggio Emilia, Italy. Talk title: Decomposing the complete graph via generalized complete mappings

06.02.2017. “Discrete Mathematics Seminar - Graphs at Ryerson", Ryerson University (ON) Canada. Talk title: f-Pyramidal Steiner Triple Systems

18.01.2016. “Discrete Mathematics Seminar - Graphs at Ryerson", Ryerson University (ON) Canada. Talk title: Cycle systems and parallel classes

10.04.2015. “Ottawa-Carleton Discrete Mathematics Seminar”, Carleton University (ON) Canada. Talk title: Resolvable cycle decompositions and their symmetries

12.02.2015. “Discrete Mathematics Seminar”, York University (ON) Canada. Talk title: 2-Factorizations and their symmetries

03.11.2014. “Discrete Mathematics Seminar - Graphs at Ryerson", Ryerson University (ON) Canada. Talk title: Factorizations, graph labelings and symmetries

03.04.2014. “Seminari 2014”, Università “Federico II” di Napoli, Italy. Talk title: Cycle decompositions and symmetries

20.06.2013. “Seminario di Algebra e Geometria”, University Sapienza of Rome, Rome, Italy. Talk title: Cycle decompositions with a nice automorphism group

20.07.2011. “I Seminari del Dipartimento a.a. 2010 – 2011”, Università degli Studi di Perugia, Italy. Talk title: Metodi algebrici per la costruzione di disegni combinatorici con un alto grado di simmetria

Teaching Activities

2022-23. PhD in Mathematics at University of Modena and Reggio Emilia. Course: New directions in Designs and Graphs (co-teacher, 12 hours out of 40 hours in total)

2021-22. PhD in Mathematics at University of Modena and Reggio Emilia. Course: Designs, Graphs and their Applications (co-teacher, 6 hours out of 40 hours in total)

2020-21. PhD in Information Engineering, University of Brescia, Italy. Course: Graph Labelings, Colorings And Their Applications (co-teacher, 8 hours out of 16 hours in total)

2020-21. Master di I livello “Matematica per l’accesso nei ruoli di docente della scuola secondaria classe A26”, Università degli Studi di Brescia, Italia. Course: Matematica Discreta (co-titolare)

2019–present. Bachelor's Degrees in Management Engineering, University of Brescia, Italy. Course: Algebra and Geometry

2019–21. Bachelor's Degrees in Industrial Automation Engineering, University of Brescia, Italy. Course: Algebra and Geometry

2017–18. Lecturer – Bachelor's Degree in Engineering and Management, Faculty of Engineering, University of Padova, Italy. Course: Fondamenti di Algebra Lineare e Geometria (Linear Algebra and Geometry)

2017. Lecturer – Bachelor’s and Master Degree in Computer Science, Università degli Studi di Verona, Italy. Course: An Introduction to Orthogonal Arrays and their applications with Codes (12 hours, language: English)

2013–14. Lecturer – Bachelor's Degree in Mechanical Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Linear Algebra

2012–13. Lecturer – Bachelor's Degree in Mechanical Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria (Linear Algebra and Geometry)

2011–12. Lecturer – Bachelor's Degree in Mechanical Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria (Linear Algebra and Geometry)

2011–12. Lecturer – Bachelor's Degree in Computer Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria e Combinatoria (Linear Algebra and Discrete Mathematics)

2010–11. Teaching Assistant – Bachelor's Degree in Mechanical Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria

2010–11. Teaching Assistant – Bachelor's Degree in Civil Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria

2010–11. Teaching Assistant – Bachelor's Degree in Computer Engineering, Faculty of Engineering, University Roma Tre, Rome, Italy. Course: Geometria e Combinatoria

2007–08. Teaching Assistant – Bachelor's Degree in Computer Engineering, Faculty of Science, Università degli Studi di Perugia, Italy. Course: Discrete Mathematics I

Service

Referee for Mathematical Reviews/MathSciNet - Australasian Journal of Combinatorics - Journal of Combinatorial Designs - Discrete Mathematics - The Electronic Journal of Combinatorics - Discrete Applied Mathematics - Designs, Codes and Cryptography - Journal of Combinatorial Theory A – Algebraic Combinatorics - European Journal of Combinatorics

Referee for REPRISE (Register of Expert Peer Reviewers for Italian Scientific Evaluation)

## Parole chiave libere (5)

AUTOMORPHISMS OF COMBINATORIAL STRUCTURES

DESIGN THEORY; GRAPH DECOMPOSITION

GRAPH FACTORIZATIONS, PACKINGS AND COVERINGS

GRAPH LABELINGS

REGULAR STEINER TRIPLE SYSTEMS

No Results Found

## Linee di ricerca

No Results Found