A n-vertex graph is said to be decomposable if for any partition (λ1,…, λp) of the integer n,
there exists a sequence (V1,…, Vp) of connected vertex-disjoint subgraphs with| Vi|= λi. In …

In this article, we deal with graphs modelling interconnection networks of parallel systems
(parallel computers, networks of workstations, etc.). We want to share the nodes of such a …

Let G be a graph of order n and r, 1≤ r≤ n, a fixed integer. G is said to be r-vertex
decomposable if for each sequence (n1,…, nr) of positive integers such that n1+⋯+ nr= n …

A graph G of order n is called arbitrarily partitionable (AP for short) if, for every sequence
(n_1,...,n_k) of positive integers with n_1+⋯+n_k=n, there exists a partition (V_1,...,V_k) of …

A graph G of order n is said to be arbitrarily vertex decomposable if for each sequence (n
1,..., nk) of positive integers such that n 1+···+ nk= n there exists a partition (V 1,..., V k) of the …

A graph\(G\) of order\(n\) is said to be arbitrarily vertex decomposable if for each
sequence\((n_ {1},\ldots, n_k)\) of positive integers such that\(n_ {1}+\ldots+ n_ {k}= n\) there …

A graph G=(V, E) is arbitrarily vertex decomposable if for any sequence τ of positive integers
adding up to| V|, there is a sequence of vertex-disjoint subsets of V whose orders are given …

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,
aₖ) of positive integers such that a₁+...+ aₖ= n there exists a partition (V₁,..., Vₖ) of the …

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1,…,
nk) of positive integers with n1+⋯+ nk= n, there exists a partition (V1,…, Vk) of the vertex set …

Résumé Les problèmes de décomposition de graphes sont au coeur de la théorie des
graphes. Dans cette thèse nous étudions le problème Graphe_Partition qui, étant donné un …