Partitioning the Cartesian product of an arbitrarily partitionable graph and a complete graph

Olivier Baudon (1) , Julien Bensmail (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A graph G is arbitrarily partitionable (AP for short) if for every sequence (n_1, ..., n_p) of positive integers summing up to |V(G)| there exists a partition (V_1, ..., V_p) of V(G) such that G[V_i] is a connected graph on n_i vertices for every i in {1,...,p}. We show that the Cartesian product G x K_l is AP whenever G is AP and K_l is a complete graph on l >= 1 vertices.

Mots clés: graph; arbitrary partition; cartesian product; complete graph

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Julien Bensmail. Partitioning the Cartesian product of an arbitrarily partitionable graph and a complete graph. 2012. ⟨hal-00759291⟩