Geodesic
Cyclic and symmetric hamiltonian cycle systems of the complete multipartite graph: even number of parts
Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 219-233.

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In this paper, we present a complete solution to the existence problem for a cyclic hamiltonian cycle system for the complete multipartite graph with an even number of parts all of the same cardinality. We also give necessary and sufficient conditions for the system to be symmetric as well.
DOI : 10.26493/1855-3974.847.af5
Keywords: Hamiltonian cycle, cyclic cycle system, symmetric hamiltonian cycle system, complete multipartite graph 
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Francesca Merola; Anita Pasotti; Marco Antonio Pellegrini. Cyclic and symmetric hamiltonian cycle systems of the complete multipartite graph: even number of parts. Ars Mathematica Contemporanea, Tome 12 (2017) no. 2, pp. 219-233. doi : 10.26493/1855-3974.847.af5. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.847.af5/

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