Drawing inspiration from a well-known conjecture of Chv\'atal on a toughness threshold
guaranteeing graph Hamiltonicity, we investigate toughness properties of so-called …

A simple graph $ G=(V, E) $ on $ n $ vertices is said to be recursively partitionable (RP) if $
G\simeq K_1 $, or if $ G $ is connected and satisfies the following recursive property: for …

A graph G of order n is arbitrarily partitionable (AP) if, for every sequence (n1,..., np)
partitioning n, there is a partition (V1,..., Vp) of V (G) such that G [Vi] is a connected graph of …

This thesis is dedicated to the study of two families of graph partition problems. First, we
consider the problem of vertex-partitioning a graph into connected subgraphs. Namely …

A graph G on n vertices is arbitrarily partitionable (AP for short) if for every partition (λ1,..., λp)
of n (that is, λ1+...+ λp= n), the vertex set V (G) can be partitioned into p parts V1,..., Vp such …

A graph G=(V, E) of order n is said to be arbitrarily partitionable if for each sequence λ=(λ 1,
λ 2,…, λ p) of positive integers with λ 1+…+ λ p= n, there exists a partition (V 1, V 2,…, V p) of …

Abstract A graph G=(V, E) is arbitrarily partitionable 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 …

This document describes some of the research work I have been conducting since the
defence of my Ph. D. thesis at Université de Bordeaux, France, back in June 2014. It is more …

A connected graph G with order n>= 1 is said to be recursively arbitrarily partitionable (R-AP
for short) if either it is isomorphic to K_1, or for every sequence (n_1,..., n_p) of positive …

Abstract Let G=(V, E) be a graph of order n, and λ=(λ 1, λ 2,…, λ p) a sequence of positive
integers. The sequence λ is admissible for G if λ 1+⋯+ λ p= n. Such an admissible sequence …