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math.CO2025
Some bounds on the number of non isomorphic cyclic k-cycle systems of the complete graph
Lotrenzo Mella, Gloria Rinaldi
In a recent paper (2024) M. Buratti and M.E:Muzychuck have established some lower bounds on the number of non isomorphic cyclic Steiner Triple Systems of order (mod …
math.CO2022
Quaternionic factorizations and complete sets of rainbow spanning trees
Gloria Rinaldi
A factorization of a complete graph on vertices is said to be regular if it posseses an automorphism group acting sharply transitively on the vertex-set. The probl…
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,…