Vertex-weighted graphs of maximum degree Δ admit (1+ε)-EQ1 k-colorings for k = O((1/ε² log(1/ε)) Δ) and 2-EQ1 colorings for k ≥ Δ+1, both computable in polynomial time.
Proof of a conjecture of
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Equitable Colorings of Vertex-Weighted Graphs
Vertex-weighted graphs of maximum degree Δ admit (1+ε)-EQ1 k-colorings for k = O((1/ε² log(1/ε)) Δ) and 2-EQ1 colorings for k ≥ Δ+1, both computable in polynomial time.