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G-2013-83

A Note on r-Equitable k-Colorings of Trees

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A graph G=(V,E) is r-equitably k-colorable if there exists a partition of V into k independent sets V1,V2,,Vk such that ||Vi||Vj||r for all i,j{1,2,,k}. In this note, we show that if two trees T1 and T2 of order at least two are r-equitably k-colorable for r1 and k3, then all trees obtained by adding an arbitrary edge between T1 and T2 are also r-equitably k-colorable.

, 8 pages

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