Equitable Colorings of $K_4$-minor-free Graphs

Coloration équitable des graphes sans $K_4$-mineur

Rémi de Joannis de Verclos (1) , Jean-Sébastien Sereni (2, 3)

1 G-SCOP_OC - Optimisation Combinatoire
2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 ORPAILLEUR - Knowledge representation, reasonning

We demonstrate that for every positive integer ∆, every K_4-minor-free graph with maximum degree ∆ admits an equitable coloring with k colors wherek ≥ (∆+3)/2. This bound is tight and confirms a conjecture by Zhang and Whu. We do not use the discharging method but rather exploit decomposition trees of K 4-minor-free graphs.

Mots clés: K_4-minor-free graph; maximum degree; equitable coloring; series-parallel graph

Domaines: Combinatoire [math.CO]

Rémi de Joannis de Verclos, Jean-Sébastien Sereni. Equitable Colorings of $K_4$-minor-free Graphs. Journal of Graph Algorithms and Applications, 2017, 21 (6), pp.1091 - 1105. ⟨10.7155/jgaa.00451⟩. ⟨hal-01483972⟩