Abstract

A graph G is equitably (k; d)-choosable if, for any k-uniform list assignment L, G admits a d-relaxed coloring f such that f(v) ∈ L(v) for all v ∈ V (G) and each color appears on at most ⌈|G|/k ⌉ vertices. It is proved that every graph G with θ(G) ≤ 6 is equitably (3; 1)-choosable and equitably (2; 2)-choosable.

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