Proper Hamiltonian Paths in Edge-Colored Multigraphs

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 path is a path 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 path, depending on several parameters such as the number of edges, the rainbow degree, etc.