Distributed Near-Equitable Coloring in the LOCAL Model

For an $n$-vertex graph of maximum degree $Δ$, an equitable $(Δ+1)$-coloring is a proper coloring all of whose color classes have size $σ= n/(Δ+1)$ up to rounding. Known algorithms for relaxations of this target aggregate along a spanning structure, at cost scaling with the diameter $D$. We study ne