Decompositions of the wreath product of certain directed graphs into directed hamiltonian cyclesLacaze-Masmonteil, Alice (Avtor) wreath productdecompositionshamiltonian cycledirected graphsWe affirm several special cases of a conjecture that first appears in Alspach et al. (1987) which stipulates that the wreath (lexicographic) product of two hamiltonian decomposable di- rected graphs is also hamiltonian decomposable. Specifically, we show that the wreath product of hamiltonian decomposable directed graph G, such that |V (G)| is even and |V (G)| ⩾ 3, with a directed m-cycle such that m ⩾ 4 or the complete symmetric directed graph on m vertices such that m ⩾ 3, is hamiltonian decomposable. We also show the wreath product of a directed n-cycle, where n is even, with a directed m-cycle, where m ∈ {2, 3}, is not hamiltonian decomposable.Založba Univerze na Primorskem20262026-03-17 11:19:31Članek v reviji22783UDK: 51eISSN: 1855-3974DOI: 10.26493/1855-3974.3471.51fsl