On the Cartesian product of an arbitrarily partitionable graph and a traceable graph
Résumé
A graph G of order n is called arbitrarily partitionable (AP, for short) if, for every sequence τ = (n1 , . . . , nk ) of positive integers that sum up to n, there exists a partition (V1 , . . . , Vk ) of the vertex set V (G) such that each set Vi induces a connected subgraph of order ni. A graph G is called AP+1 if, given a vertex u ∈ V (G) and an index q ∈ {1, . . . , k}, such a partition exists with u ∈ Vq . We consider the Cartesian product of AP graphs. We prove that if G is AP+1 and H is traceable, then the Cartesian product GxH is AP+1. We also prove that GxH is AP, whenever G and H are AP and the order of one of them is not greater than four.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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