A note on relaxed equitable coloring of graphs

Authors:
Hao Fan;H. A. Kierstead;Guizhen Liu;Theodore Molla;Jian-Liang Wu;Xin Zhang
Affiliations:
School of Mathematics, Shandong University, Jinan 250100, China;School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA;School of Mathematics, Shandong University, Jinan 250100, China;School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA;School of Mathematics, Shandong University, Jinan 250100, China;School of Mathematics, Shandong University, Jinan 250100, China
Venue:
Information Processing Letters
Year:
2011

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Abstract

In this note we introduce the concept of equitable d-relaxed coloring. We prove that each graph with maximum degree at most r admits an equitable 1-relaxed r-coloring and provide a polynomial-time algorithm for constructing such a coloring.