Exact square coloring of subcubic planar graphs - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete Applied Mathematics Année : 2021

Exact square coloring of subcubic planar graphs

Résumé

We study the exact square chromatic number of subcubic planar graphs. An exact square coloring of a graph G is a vertex-coloring in which any two vertices at distance exactly 2 receive distinct colors. The smallest number of colors used in such a coloring of G is its exact square chromatic number, denoted $\chi^{\sharp 2}(G)$. This notion is related to other types of distance-based colorings, as well as to injective coloring. Indeed, for triangle-free graphs, exact square coloring and injective coloring coincide. We prove tight bounds on special subclasses of planar graphs: subcubic bipartite planar graphs and subcubic K 4-minor-free graphs have exact square chromatic number at most 4. We then turn our attention to the class of fullerene graphs, which are cubic planar graphs with face sizes 5 and 6. We characterize fullerene graphs with exact square chromatic number 3. Furthermore, supporting a conjecture of Chen, Hahn, Raspaud and Wang (that all subcubic planar graphs are injectively 5-colorable) we prove that any induced subgraph of a fullerene graph has exact square chromatic number at most 5. This is done by first proving that a minimum counterexample has to be on at most 80 vertices and then computationally verifying the claim for all such graphs.
Fichier principal
Vignette du fichier
exact_square_coloring_subcubic.pdf (449.31 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02925881 , version 1 (01-09-2020)
hal-02925881 , version 2 (30-12-2020)
hal-02925881 , version 3 (24-01-2021)

Identifiants

Citer

Florent Foucaud, Hervé Hocquard, Suchismita Mishra, Narayanan Narayanan, Reza Naserasr, et al.. Exact square coloring of subcubic planar graphs. Discrete Applied Mathematics, 2021, 293, pp.74-89. ⟨10.1016/j.dam.2021.01.007⟩. ⟨hal-02925881v3⟩
242 Consultations
211 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More