On the hyperbolicity of bipartite graphs and intersection graphs - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2015

On the hyperbolicity of bipartite graphs and intersection graphs

Résumé

Hyperbolicity is a measure of the tree-likeness of a graph from a metric perspective. Recently , it has been used to classify complex networks depending on their underlying geometry. Motivated by a better understanding of the structure of graphs with bounded hyperbolicity, we here investigate on the hyperbolicity of bipartite graphs. More precisely, given a bipartite graph B = (V0 ∪ V1 , E) we prove it is enough to consider any one side Vi of the bipartition of B to obtain a close approximate of its hyperbolicity δ(B) — up to an additive constant 2. We obtain from this result the sharp bounds δ(G) − 1 ≤ δ(L(G)) ≤ δ(G) + 1 and δ(G) − 1 ≤ δ(K(G)) ≤ δ(G) + 1 for every graph G, with L(G) and K(G) being respectively the line graph and the clique graph of G. Finally, promising extensions of our techniques to a broader class of intersection graphs are discussed and illustrated with the case of the biclique graph BK(G), for which we prove (δ(G) − 3)/2 ≤ δ(BK(G)) ≤ (δ(G) + 3)/2.
Fichier principal
Vignette du fichier
bipartite.pdf (324.59 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01220132 , version 1 (24-10-2015)
hal-01220132 , version 2 (12-07-2016)

Identifiants

  • HAL Id : hal-01220132 , version 1

Citer

David Coudert, Guillaume Ducoffe. On the hyperbolicity of bipartite graphs and intersection graphs. [Research Report] INRIA Sophia Antipolis - Méditerranée; I3S; Universite Nice Sophia Antipolis; CNRS. 2015, pp.12. ⟨hal-01220132v1⟩
312 Consultations
522 Téléchargements

Partager

Gmail Facebook X LinkedIn More