Every d-degenerate graph with at least beta-Delta vertices has an equitable tree-k-coloring for every k at least alpha-d, for twelve explicit (alpha, beta) pairs such as (8,56) and (52,6).
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Equitable tree-$O(d)$-coloring of $d$-degenerate graphs
Every d-degenerate graph with at least beta-Delta vertices has an equitable tree-k-coloring for every k at least alpha-d, for twelve explicit (alpha, beta) pairs such as (8,56) and (52,6).