For every ζ > 20.5 there is a c such that any bipartite graph with Δ ≥ c and at least ζΔ vertices has equitable chromatic number at most ⌈Δ/2⌉ + 1.
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Equitable coloring of large bipartite graphs
For every ζ > 20.5 there is a c such that any bipartite graph with Δ ≥ c and at least ζΔ vertices has equitable chromatic number at most ⌈Δ/2⌉ + 1.