Proper Hamiltonian Paths in Edge-Colored Multigraphs

Raquel Águeda (1) , Valentin Borozan (2) , Marina Groshaus (3) , Yannis Manoussakis (2) , Gervais Mendy (2) , Leandro Montero (2)

1 Departamento de Análisis Económico y Finanzas, Universidad de Castilla, La Mancha 45071 Toledo, Spain.
2 LRI - Laboratoire de Recherche en Informatique
3 Departamento de Computación [Buenos Aires]

A $c$-edge-coloured multigraph has each edge coloured with one of the $c$ available colours where no two parallel edges have the same colour. 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 a multigraph to have a proper Hamiltonian path, depending on several parameters such as the number of edges, the rainbow degree, etc.

Mots clés: Multigraph; Proper Hamiltonian Path; Edge-Colored Graph

Domaines: Mathématique discrète [cs.DM]

Raquel Águeda, Valentin Borozan, Marina Groshaus, Yannis Manoussakis, Gervais Mendy, et al.. Proper Hamiltonian Paths in Edge-Colored Multigraphs. 2013. ⟨hal-00847916v2⟩