5 papers
Banff designs: difference methods for coloring incidence graphs
Marco Buratti, Francesca Merola, Anamari Nakic +1
We present some results on the harmonious colorings of the Levi graph of a -design, focusing on Steiner -designs. It is easily seen that the harmonious chromatic number of su…
Cyclic cycle systems of the complete multipartite graph
Andrea Burgess, Francesca Merola, Tommaso Traetta
In this paper, we study the existence problem for cyclic -cycle decompositions of the graph , the complete multipartite graph with parts of size , and give nec…
Fano Kaleidoscopes and their generalizations
Marco Buratti, Francesca Merola
In this work we introduce Fano Kaleidoscopes, Hesse Kaleidoscopes and their generalizations. These are a particular kind of colored designs for which we will discuss general theory…
Cyclic hamiltonian cycle systems of the complete multipartite graph: even number of parts
Francesca Merola, Anita Pasotti, Marco Antonio Pellegrini
A hamiltonian cycle system (HCS, for short) of a graph is a partition of the edges of into hamiltonian cycles. A HCS is cyclic when it is invariant under a cyclic permutati…
Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles
Francesca Merola, Tommaso Traetta
It is conjectured that for every pair of odd integers greater than 2 with , there exists a cyclic two-factorization of having exac…