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Proper Hamiltonian Paths in Edge-Coloured Multigraphs (1406.5376v1)
Published 20 Jun 2014 in cs.DM and math.CO
Abstract: 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.