Préaffectation de sommets dans les graphes arbitrairement partitionnables
Résumé
A graph G of order n is said arbitrarily partitionable if for every partition (n_1, ..., n_k) of n, we can partition the vertex set of G into k subsets (V_1, ..., V_k) such that for every i in [1,k], the subgraph of G induced by V_i is connected and of order n_i. This thesis deals principally with a stronger version of arbitrary partitionability, said with one preaffecting, which allows us to force the membership of an arbitrary vertex of G into a particular subset of its vertex partition whose size has been chosen beforehand. Graphs which are arbitrarily partitionable this way being 2-connected, we also study arbitrary partitionability of 2-connected graphs, focusing mainly on those which can be built using a cartesian product of two arbitrarily partitionable graphs.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...