Marco Buratti

**Academic Experience**

- 2006 to current: Full Professor of Geometry at the Faculty of Engineering of the University of Perugia, Italy
- 1999 till 2006: Associate Professor of Geometry at the Faculty of Engineering of the University of Perugia, Italy
- 1991 till 1999: Assistant Professor of Geometry at the Faculty of Engineering of the University of L'Aquila, Italy

**Scientific interest**

Constructions of combinatorial designs with a rich automorphism group

**Citations**

1324 citations by 490 documents; h-index 22 (Scopus, last update: August, 2019)

**Education**

1985. Master degree in Mathematics with excellence
at the *University La Sapienza* of Rome

**Awards**

Hall Medal 1998 *For outstanding contributions in Combinatorics and its Applications*. Received at the University of Canterbury during the
*17th British Combinatorial Conference* (July, 1999)

**Membership and Editorial Work**

- Associate Editor of
*Discrete Mathematics*since 2013 - Editor in chief of
*Bulletin of the Institute of Combinatorics and its Applications*since 2016 - Member of U.M.I. (
*Unione Matematica Italiana*) from 1992 to 2016 - Fellow of the Institute of Combinatorics and its Applications since 1994
- Council Member of the
*Institute of Combinatorics and its Applications*since 2010 - Member of the Editorial Board of the
*Journal of Combinatorial Designs*since 1999 - Member of the Editorial Board of the
*Designs, Codes and Cryptography*since 2017 - Member of the Editorial Board of the
*Art of Discrete Applied Mathematics*since 2017

**List of publications on international
journals **

- [98] F. Salassa, G. Dragotto, T. Traetta, M Buratti and F. Della Croce,
*Merging Combinatorial Design and Optimization: the Oberwolfach Problem*, submitted - [97] M. Buratti, A. Nakic and A. Wassermann,
*Graph decompositions over projective geometries*, submitted - [96] M. Buratti,
*Tiling rings with precious differences*, submitted - [95] M. Buratti, M. Kiermaier, S. Kurz, A. Nakic, and A. Wassermann,
*q-analogs of group divisible designs*, submitted - [94]M. Buratti and D. Jungnickel,
*Partitioned difference families versus Zero difference balanced functions*, Designs, Codes and Cryptography, DOI: 10.1007/s10623-019-00632-x - [93] M. Buratti,
*Hadamard partitioned difference families and their descendants*, Cryptography and Communications 11 (2019), 557-562. - [92] M. Buratti and A. Nakic,
*Designs over finite fields by difference methods*, Finite Fields Appl. 57 (2019), 128-138. - [91] M. Buratti and F. Merola,
*Fano Kaleidoscopes and their generalizations*, Des. Codes Cryptogr. 87 (2019), 769-784. - [90] M. Buratti,
*On disjoint (v, k, k-1) difference families*, Des. Codes Cryptogr. 87 (2019), 745-755. - [89] M. Buratti,
*On silver and golden optical orthogonal codes*, Art Discrete Appl. Math. 1 (2018), #P2.02 - [88] M. Buratti and A. Wassermann,
*On decomposability of cyclic triple systems*, Australas. J. Combin. 71 (2018), 184-195. - [87] S. Bonvicini and M. Buratti,
*Octahedral, dicyclic and special linear solutions of some Hamilton-Waterloo problems*, Ars Math. Contemp. 14 (2018), 1-14. - [86] M. Buratti, H. Cao, D. Dai and T. Traetta,
*A complete solution to the existence of (k, λ)-cycle frames of type g*, J. Combin. Des. 25 (2017), 197-230.^{u} - [85] M. Buratti, G. Rinaldi and T. Traetta,
*3-pyramidal Steiner triple systems*, Ars Math. Contemp. 13 (2017), 95-106. - [84] M. Buratti, S. Costa and X. Wang,
*New i-perfect cycle decompositions via vertex colorings of graphs*, J. Combin. Des. 24 (2016), 495-513. - [83] M. Buratti and P. Danziger,
*A cyclic solution for an infinite class of Hamilton-Waterloo problems*, Graphs Combin.**32**(2016), 521-531. - [82] M. Buratti, G.J. Lovegrove and T. Traetta,
*On the full automorphism group of a Hamiltonian cycle system of odd order*, Graphs Combin. 31 (2015), 1855-1865. - [81] M. Buratti and T. Traetta,
*The structure of 2-pyramidal 2-factorizations*, Graphs Combin.**31**(2015), 523-535. - [80] R.A. Bailey, M. Buratti, G. Rinaldi and T. Traetta,
*On 2-pyramidal Hamiltonian cycle systems*, Bull. Belg. Math. Soc. Simon Stevin**21**(2014), 747-758. - [79] M. Buratti and F. Merola,
*Hamiltonian cycle systems which are both cyclic and symmetric*, J. Combin. Des**22**(2014), 367-390. - [78] M. Buratti, G. Rinaldi and T. Traetta,
*Some results on 1-rotational Hamiltonian cycle systems*, J. Combin. Des.**22**(2014), 231-251. - [77] M. Buratti and A. Pasotti,
*Cyclic kite-designs of order v that are ciclically embedded into a cyclic (v,4,2)-design*, Quaderni di Matematica. - [76] M. Buratti, S. Capparelli, F. Merola, G. Rinaldi and T. Traetta,
*A collection of results on Hamiltonian cycle systems with a nice automorphism group*, Electronic Notes in Discrete Mathematics**40**(2013), 245-252. - [75] E.Brugnoli and M. Buratti,
*New designs by changing ... the signs*, Electronic Notes in Discrete Mathematics**40**(2013) 49{52. - [74] M. Buratti, A. Pasotti and D. Wu,
*On optimal (v,5,2,1) optical orthogonal codes*, Des. Codes Cryptogr.**68**(2013), 349-371. - [73] M. Buratti and F. Merola,
*Dihedral Hamiltonian cycle systems of the cocktail party graph*, J. Combin. Des.**21**(2013), 1-23. - [72] M. Buratti and T. Traetta,
*2-starters, graceful labelings, and a doubling construction for the Oberwolfach Problem*, J. Combin. Des.**20**(2012), 483-503. - [71] S. Bonvicini, M. Buratti, G. Rinaldi and T. Traetta,
*Some progress on 1-rotational Steiner triple systems*, Des. Codes Cryptogr.**62**(2012), 63-78. - [70] M. Buratti, Y. Wei, D. Wu, P. Fan and M. Cheng,
*Relative difference families with variable block sizes and their related OOCs*, IEEE Trans. Inform. Theory,**57**(2011), 7489-7497. - [69] M. Buratti, K. Momihara and A. Pasotti,
*New results on optimal (v,4,2,1) optical orthogonal codes*, Des. Codes Cryptogr.**58**(2011), 89-109. - [68] M. Buratti, J. Yan and C. Wang,
*From a 1-rotational RBIBD to a partitioned difference family*, Electronic J. Combin.**17**(2010). - [67] M. Buratti,
*Difference families and Frobenius groups*, RIMS Kokyuroku**1687**(2010), 71-76. - [66] M. Buratti and D. Ghinelli,
*On disjoint (3t,3,1) difference families*, J. Statist. Plann. Inference**140**(2010), 1918-1922. - [65] M. Buratti, S. Capparelli and A. Del Fra,
*Cyclic Hamiltonian cycle systems of the λ-fold complete and cocktail party graphs*, European J. Combin.**31**(2010), 1484-1496. - [64] M. Buratti and A. Pasotti,
*Further progress on difference families with block size 4 or 5*, Des. Codes Cryptogr.**56**(2010), 1-20. - [63] M. Buratti and A. Pasotti,
*Combinatorial designs and the theorem of Weil on multiplicative character sums*, Finite Fields Appl.**15**(2009), 332-344. - [62]
M. Buratti and G. Rinaldi,
*A non-existence result on cyclic cycle-decompositions of the cocktail party graph*, Discrete Math.**309**(2009), 4722-4726. - [61] K. Momihara and M. Buratti,
*Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes*, IEEE Trans. Inform. Theory**55**(2009), 514-523. - [60] M. Buratti, A. Bonisoli and G. Rinaldi,
*Sharply transitive decompositions of complete graphs into generalized Petersen graphs*, Innov. Incidence Geom.**6/7**(2009), 95-109. - [59] S.L. Wu and M. Buratti,
*A complete solution to the existence problem for 1-rotational k-cycle systems of K*, J. Combin. Des._{v}**17**(2009), 283-293. - [58] M. Buratti and A. Pasotti,
*On perfect Γ-decompositions of the complete graph*, J. Combin. Des.**17**(2009), 197-209. - [57] M. Buratti and L. Gionfriddo,
*Strong difference families over arbitrary groups*, J. Combin. Des.**16**(2008), 443-461. - [56] M. Buratti and G. Rinaldi,
*1-rotational k-factorizations of the complete graph and new solutions to the Oberwolfach problem*, J. Combin. Des.**16**(2008), 87-100. - [55] M. Buratti and N.J. Finizio,
*Existence results for 1-rotational resolvable Steiner 2-designs with block size 6 or 8*, Bull. Inst. Combin. Appl.**50**(2007), 29-44. - [54] M. Buratti, N.J. Finizio, M. Greig and B.J. Travers,
*Z-cyclic (t,8) GWhD(v), t=2,4*, Util. Math.**72**(2007), 125-138. - [53] A. Bonisoli, M. Buratti and G. Mazzuoccolo,
*Doubly transitive 2-factorizations*, J. Combin. Des.**15**(2007), 120-132. - [52] M. Buratti and A. Pasotti,
*Graph decompositions with the use of difference matrices*, Bull. Inst. Combin. Appl.**47**(2006), 23-32. - [51] M. Buratti, F. Rania and F. Zuanni,
*Some constructions for cyclic perfect cycle systems*, Discrete Math.**299**(2005), 33-48. - [50] M. Buratti and G. Rinaldi,
*On sharply vertex transitive 2-factorizations of the complete graph*, J. Combin. Theory Ser. A**111**(2005), 245-256. - [49] M. Buratti,
*Cycle decompositions with a sharply vertex transitive automorphism group*, Matematiche (Catania)**59**(2004), 91-105. - [48] M. Buratti and A. Del Fra,
*Cyclic Hamiltonian cycle systems of the complete graph*, Discrete Math.**279**(2004), 107-119. - [47] R.J.R. Abel and M. Buratti,
*Some progress on (v,4,1) difference families and optical orthogonal codes*, J. Combin. Theory Ser. A**106**(2004), 59-75. - [46] M. Buratti,
*Existence of 1-rotational k-cycle systems of the complete graph*, Graphs Combin.**20**(2004), 41-46. - [45] M. Buratti and A. Del Fra,
*Semi-Boolean Steiner quadruple systems and dimensional dual hyperovals*, Adv. Geom. (2003), suppl., S254-S270. - [44] M. Buratti,
*Rotational k-cycle systems of order v<3k; another proof of the existence of odd cycle systems*, J. Combin. Des.**11**(2003), 433-441. - [43] M. Buratti and A. Del Fra,
*A lower bound on the number of semi-Boolean quadruple systems*, J. Combin. Des.**11**(2003), 229-239. - [42] M. Buratti and A. Del Fra,
*Existence of cyclic k-cycle systems of the complete graph*, Discrete Math.**261**(2003), 113-125. - [41] M. Buratti,
*Constructions for resolved designs by difference methods*, 6th Workshop on Combinatorics (Messina, 2002). Rend. Sem. Mat. Messina Ser. II 8(24) (2001/02), suppl., 19-28. - [40] M. Buratti,
*Cyclic designs with block size 4 and related optimal optical orthogonal codes*, Des. Codes Cryptogr.**26**(2002), 111-125. - [39] M. Buratti, M. Gionfriddo, L. Milazzo and V. Voloshin,
*Lower and upper chromatic numbers for BSTSs(2*, Computer Sci. J. Moldova^{h}-1)**9**(2001), 259-272. - [38] M. Buratti and F. Zuanni,
*Explicit constructions for 1-rotational Kirkman triple systems*, Util. Math.**59**(2001), 27-30. - [37] M. Buratti and F. Zuanni,
*Some observations on three classical BIBD constructions*, Discrete Math.**283**(2001), 19-26. - [36] M. Buratti,
*1-rotational Steiner triple systems over arbitrary groups*, J. Combin. Des.**9**(2001), 215-226. - [35] R.J.R. Abel, M. Buratti, M. Greig and Y. Miao,
*Constructions for rotational near resolvable block designs*, J. Combin. Des.**9**(2001), 157-181. - [34] M. Buratti and F. Zuanni,
*Perfect Cayley Designs as generalizations of Perfect Mendelsohn Designs*, Des. Codes Cryptogr.**23**(2001), 233-247. - [33] M. Buratti,
*Abelian 1-factorizations of the complete graph*, European J. Combin.**22**(2001), 291-295. - [32] M. Buratti,
*Constructions for point-regular linear spaces*, J. Statist. Plann. Inference**94**(2001), 139-146. - [31] M. Buratti,
*Some regular Steiner 2-designs with block-size 4*, Ars Combin.**55**(2000), 133-137. - [30] M. Buratti,
*Two new classes of difference families*, J. Combin. Theory Ser. A**90**(2000), 353-355. - [29] M. Buratti,
*Existence of Z-cyclic triplewhist tournaments for a prime number of players*, J. Combin. Theory Ser. A**90**(2000), 315-325. - [28] M. Buratti and F. Zuanni,
*The 1-rotational Kirkman triple systems of order 33*, J. Statist. Plann. Inference,**86/2**(2000), 369-377. - [27] M. Buratti,
*Old and new designs via difference multisets and strong difference families*, J. Combin. Des.**7**(1999), 406-425. - [26] M. Buratti,
*Pairwise balanced designs from finite fields*, Discrete Math.**208/209**(1999), 103-117. - [25] M. Buratti and F. Zuanni,
*The 1-rotational (52,4,1)-RBIBD's*, J. Combin. Math. Combin. Comput.**30**(1999), 99-102. - [24] M. Buratti and F. Zuanni,
*On singular 1-rotational Steiner 2-designs*, J. Comb. Theory Ser. A**86**(1999), 232-244. - [23] M. Buratti,
*1-rotational Kirkman triple systems generate dicyclic Steiner 2-designs with block-size 4*, Bull. Inst. Combin. Appl.**26**(1999), 91-95. - [22] M. Buratti,
*Some regular (17q,17,2) and (25q,25,3) BIBD constructions*, Des. Codes Cryptogr.**16**(1999), 117-120. - [21] M. Buratti and F. Zuanni,
*G-invariantly resolvable Steiner 2-designs which are 1-rotational over G*, Bull. Belg. Math. Soc.**5**(1998), 221-235. - [20] M. Buratti,
*Some constructions for 1-rotational BIBD's with block-size 5*, Australas. J. Combin.**17**(1998), 199-227. - [19] M. Buratti,
*Small quasimultiple of affine and projective planes; some improved bounds*, J. Combin. Des.**6**(1998), 337-345. - [18] M. Buratti,
*Recursive constructions for difference matrices and relative difference families*, J. Combin. Des.**6**(1998), 165-182. - [17] M. Buratti,
*Packing the blocks of a regular structure*, Bull. Inst. Combin. Appl.**21**(1997), 49-58. - [16] M. Buratti,
*Cyclotomic conditions leading to new Steiner 2-designs*, Finite Fields Appl.**3**(1997), 300-313. - [15] M. Buratti, G. Burosch and P.V. Ceccherini,
*A characterization of hypergraphs which are products of a finite number of edges*, Rend. Mat. Appl. (7), Roma (1997), 373-385. - [14] L. Berardi, M. Buratti and S. Innamorati,
*4-blocked Hadamard 3-designs*, Discrete Math.**174**(1997), 35-46. - [13] M. Buratti,
*Clique-colourings characterizing Hamming graphs*, Bull. Inst. Combin. Appl.**20**(1997), 57-61. - [12] M. Buratti,
*On resolvable difference families*, Des. Codes Cryptogr.**11**(1997), 11-23. - [11] M. Buratti,
*From a (G,k,1) to a (C*, Des. Codes Cryptogr._{k}⊕ G,k,1) difference family**11**(1997), 5-9. - [10] M. Buratti,
*Edge-colourings characterizing a class of Cayley Graphs and a New Characterization of Hypercubes*, Discrete Math.**161**(1996), 291-295. - [9] M. Buratti,
*A packing problem and its application to Bose's families*, J. Combin. Des.**4**(1996), 457-472. - [8] M. Buratti,
*A powerful method for constructing difference families and optimal optical orthogonal codes*, Des. Codes Cryptogr.**5**(1995), 13-25. - [7] M. Buratti,
*Constructions of (q,k,1) difference families with q a prime power and k = 4,5*, Discrete Math.**138**(1995), 169-175. - [6] M. Buratti,
*On simple radical difference families*, J. Combin. Des.**3**(1995), 161-168. - [5] M. Buratti,
*Improving two theorems of Bose on difference families*, J. Combin. Des.**3**(1995), 15-24. - [4] M. Buratti,
*Cayley, Marty and Schreier Hypergraphs*, Abh. Math. Sem. Univ. Hamburg**64**(1994), 151-162. - [3] M. Buratti,
*Schubert Graphs, Symmetric Groups and Flags of Boolean Lattices*, J. Geom.**48**(1993), 10-22. - [2] M. Buratti,
*On a property of symmetric designs of order n ≡ 2 (mod 4)*, J. Geom.**34**(1989), 30-35. - [1] M. Buratti,
*Bruck-Ryser Abstract Theorem and Symmetric Designs*, Geom. Dedicata**27**(1988), 241-250.