Partitioning powers of traceable or hamiltonian graphs

Olivier Baudon (1) , Julien Bensmail (1) , Jakub Przybylo (2) , Mariusz Woźniak (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 AGH UST - AGH University of Science and Technology [Krakow, PL]

A graph G = (V,E) is arbitrarily partitionable (AP) if for any sequence tau = (n_1, ..., n_p) of positive integers adding up to the order of G, there is a sequence of vertex-disjoints subsets of V whose orders are given by tau and which induce connected graphs. If, additionally, for any k, k <= p, of elements of tau we are allowed to prescribe k vertices belonging to the subsets with given size, we say that G is AP+k. We prove that the kth power of every traceable graph of order at least k is AP+(k-1) and that the kth power of every hamiltonian graph of order at least 2k is AP+(2k-1), and these results are tight.

Mots clés: arbitrarily partitionable graph; power of a graph; hamiltonian graph; traceable graph

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Julien Bensmail, Jakub Przybylo, Mariusz Woźniak. Partitioning powers of traceable or hamiltonian graphs. 2012. ⟨hal-00687278v1⟩