On Compatible Normal Odd Partitions in Cubic Graphs
Résumé
A normal odd partition of the edges of a cubic graph is a partition into trails of odd length (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition and internal in another trail. For each vertex, we can distinguish the edge for which this vertex is pending. Three normal odd partitions are compatible whenever these distinguished edges are distinct for each vertex. We study here this notion and show that a cubic three edge-colorable graph can always be provided with three compatible normal odd partitions. The Petersen graph have this property and we can construct other cubic graphs with chromatic index four with the same property. At last, we give a connexion with the Fan Rapaud conjecture and propose a new conjecture which, if true, would imply this conjecture.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)