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B.-L Chen.C-H.Yen Discrete Mathematics 312(2012)1512-1517 1517 Acknowledgments The authors thank Professor Ko-Wei Lih,Professor Hung-Lin Fu and the referees for many helpful comments which led References r.J.C n1510 3082008553-5537. Ye A pA A.4.No 70.pp 543 B.-L. Chen, C.-H. Yen / Discrete Mathematics 312 (2012) 1512–1517 1517 Acknowledgments The authors thank Professor Ko-Wei Lih, Professor Hung-Lin Fu and the referees for many helpful comments which led to a better version of this paper. This research was partially supported by the National Science Council of the Republic of China under the grants NSC 95-2119-M-415-001 and NSC 96-2115-M-415-005. References [1] R.L. Brooks, On colouring the nodes of a network, Proc. Cambridge Phil. Soc. 37 (1941) 194–197. [2] B.-L. Chen, K.-C. Huang, C.-H. Yen, Chromatic coloring with a maximum color class, Discrete Math. 308 (2008) 5533–5537. [3] B.-L. Chen, K.-W. Lih, P.-L. Wu, Equitable coloring and the maximum degree, Eur. J. Combin. 15 (1994) 443–447. [4] B.-L. Chen, K.-W. Lih, C.-H. Yen, Equivalence of two conjectures on equitable coloring of graphs (submitted for publication). [5] A. Hajnal, E. Szemerédi, Proof of a conjecture of Erdős, in: A. Rényi, V.T. Sós (Eds.), Combinatorial Theory and Its Applications. Vol. II, in: Colloq. Math. Soc. János Bolyai, vol. 4, North-Holland, Amsterdam, 1970, pp. 601–623. [6] H.A. Kierstead, A.V. Kostochka, Equitable versus nearly equitable coloring and the Chen–Lih–Wu conjecture, Combinatorica 30 (2010) 201–216. [7] K.-W. Lih, The equitable coloring of graphs, in: D.-Z. Du, P.M. Pardalos (Eds.), in: Handbook of Combinatorial Optimization, vol. 3, Kluwer Academic Publishers, 1998, pp. 543–566. [8] K.-W. Lih, P.-L. Wu, On equitable coloring of bipartite graphs, Discrete Math. 151 (1996) 155–160. [9] W. Meyer, Equitable coloring, Amer. Math. Monthly 80 (1973) 920–922. [10] D.B. West, Introduction to Graph Theory, second ed., Prentice-Hall, Upper Saddle River, NJ, 2001. [11] H.P. Yap, Y. Zhang, On equitable coloring of graphs, manuscript, 1996
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