From χ to χp-bounded classes - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Journal of Combinatorial Theory, Series B Année : 2023

From χ to χp-bounded classes

Résumé

χ-bounded classes are studied here in the context of star colorings and, more generally, χ pcolorings. This fits to a general scheme of sparsity and leads to natural extensions of the notion of bounded expansion class. In this paper we solve two conjectures related to star coloring (i.e. χ 2) boundedness. One of the conjectures is disproved and in fact we determine which weakening holds true. χ p-boundedness leads to more stability and we give structural characterizations of (strong and weak) χ p-bounded classes. We also generalize a result of Wood relating the chromatic number of a graph to the star chromatic number of its 1-subdivision. As an application of our characterizations, among other things, we show that for every odd integer g > 3 even hole-free graphs G contain at most ϕ(g, ω(G)) |G| holes of length g.
Fichier principal
Vignette du fichier
EHF-v1.3-revised.pdf (290.4 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03373528 , version 1 (11-10-2021)

Identifiants

Citer

Yiting Jiang, Jaroslav Nešetřil, Patrice Ossona de Mendez. From χ to χp-bounded classes. Journal of Combinatorial Theory, Series B, 2023, Robin Thomas 1962-2020, 158 (1), pp.186-209. ⟨10.1016/j.jctb.2021.05.006⟩. ⟨hal-03373528⟩
14 Consultations
49 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More