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: 34
Papers submitted for publication in refereed journals: 1
Preprint: 4
Total citations: 286 (Scopus)
H-index: 11 (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, Journal of Combinatorial Theory A 205 (2024), 105873
31. T. Traetta. A constructive solution to the Oberwolfach problem with a large cycle, Discrete Mathematics 347 (2024), 113947
32. P. Danziger, E. Mendelsohn, B. Stevens, T. Traetta. On the mini-symposium problem, Ars Math. Contemp. 24 (2024), #3.07. https://doi.org/10.26493/1855-3974.2835.8f0
33. A. Burgess, P. Danziger, T. Traetta (2024). A Survey on Constructive Methods for the Oberwolfach Problem and Its Variants. In: Colbourn, C.J., Dinitz, J.H. (eds) New Advances in Designs, Codes and Cryptography. NADCC 2022. Fields Institute Communications, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-031-48679-1_3
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. Accepted in The Art of Discrete and Applied Mathematics
Papers Submitted for Publication in Refereed Journals
35. M. Pellegrini, T. Traetta. Towards a solution of Archdeacon's conjecture on integer Heffter arrays, submitted