Rémi De Joannis de Verclos

Equitable Colorings of $K\_4$-minor-free Graphs

We demonstrate that for every positive integer $Δ$, every K\_4-minor-free graph with maximum degree $Δ$ admits an equitable coloring with k colors wherek $\ge$ ($Δ$+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.