A c-edge-colored multigraph has each edge colored with one of the c
available colors and no two parallel edges have the same color. A proper
Hamiltonian cycle is a cycle containing all the vertices of the multigraph such
that no two adjacent edges have the same color. In this work we establish
sufficient conditions for a multigraph to have a proper Hamiltonian cycle,
depending on several parameters such as the number of edges and the rainbow
degree.Comment: 13 page
