EQUITABLE LIST COLORING OF GRAPHS

@inproceedings{Wang1997EQUITABLELC,
  title={EQUITABLE LIST COLORING OF GRAPHS},
  author={Wei-Fan Wang and Ko-Wei Lih},
  year={1997}
}
A graph G is equitably k-choosable if, for any k-uniform list assignment L, G admits a proper coloring π such that π(v) ∈ L(v) for all v ∈ V (G) and each color appears on at most |G|/k vertices. It was conjectured in [8] that every graph G with maximum degree ∆ is equitably k-choosable whenever k ≥ ∆ + 1. We prove the conjecture for the following cases: (i) ∆ ≤ 3; (ii) k ≥ (∆ − 1). Moreover, equitably 2-choosable graphs are completely characterized. 

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