Characterization of (2m, m)-paintable graphs

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This paper proves that for any graph G and any positive integer m, G is (2m, m)-paintable if and only if G is 2-paintable.It was asked by Zhu in 2009 whether k-paintable graphs are (kin, m)-paintable for any positive integer m.Our result answers this question in the affirmative for k =2.
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