  Given a $c$-edge-coloured multigraph, a proper Hamiltonian path is a path
that contains all the vertices of the multigraph such that no two adjacent
edges have the same colour. In this work we establish sufficient conditions for
an edge-coloured multigraph to guarantee the existence of a proper Hamiltonian
path, involving various parameters as the number of edges, the number of
colours, the rainbow degree and the connectivity.
