Some Properties of Minimal Arbitrarily Partitionable Graphs - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue The Australasian Journal of Combinatorics Année : 2023

Some Properties of Minimal Arbitrarily Partitionable Graphs

Résumé

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 that G[Vi] has order λi and is connected for every i∈{1,...,p}. Several aspects of AP graphs have been investigated to date, including structural and algorithmic aspects, and variants. This work is dedicated to minimal AP graphs, which are those AP graphs that are not spanned by any proper AP subgraph. In particular, we pursue previous investigations by Ravaux and Baudon, Przybyło, and Woźniak, who established that minimal AP graphs are not all trees, but conjectured that they should all be somewhat sparse. In that line, we investigate several aspects of minimal AP graphs, including their minimum degree, their maximum degree, and their clique number. Some of the results we establish arise from an exhaustive list we give of all minimal AP graphs of order at most 10. We also address new questions on the structure of minimal AP graphs.
Fichier principal
Vignette du fichier
minAP-plain.pdf (307.66 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03654327 , version 1 (28-04-2022)

Identifiants

  • HAL Id : hal-03654327 , version 1

Citer

Julien Bensmail. Some Properties of Minimal Arbitrarily Partitionable Graphs. The Australasian Journal of Combinatorics, 2023, 86 (1), pp.149-168. ⟨hal-03654327⟩
73 Consultations
45 Téléchargements

Partager

Gmail Facebook X LinkedIn More