Equitable colorings of $K_4$-minor-free graphs

Rémi de Joannis de Verclos, Jean-Sébastien Sereni
2017 Journal of Graph Algorithms and Applications  
We demonstrate that for every positive integer ∆, every K 4 -minor-free graph with maximum degree ∆ admits an equitable coloring with k colors where k ∆+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.
doi:10.7155/jgaa.00451 fatcat:kp2bugfz7ba77mmgu2ym7numgm