Equitable Colourings of d-degenerate Graphs
Alexandr V. Kostochka, Kittikorn Nakprasit · Combinatorics Probability Computing · 2003
A proper vertex coloring of a graph is called equitable if the sizes of colour classes differ by at most 1. In this paper, we find the minimum number l=l(d, Δ) such that every d-degenerate graph with maximum degree at most Δ admits an equitable t-colouring for every t[ges ]l when Δ[ges ]27d.