Discussiones Mathematicae Graph Theory 27(1) (2007) 159-174
doi: 10.7151/dmgt.1352

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IMPROVED UPPER BOUNDS FOR NEARLY ANTIPODAL CHROMATIC NUMBER OF PATHS

Yu-Fa Shena, Guo-Ping Zhenga, Wen-Jie Heb

aDepartment of Mathematics and Physics
Hebei Normal University of Science and Technology
Qinhuangdao 066004, P.R. China
bApplied Mathematics Institute
Hebei University of Technology
Tianjin 300130, P.R. China
e-mail: syf030514@163.com (Yu-Fa Shen).

Abstract

For paths Pn, G. Chartrand, L. Nebeský and P. Zhang showed that ac′(Pn) ≤ (n-2)(n-3)/2+2 for every positive integer n, where ac′(Pn) denotes the nearly antipodal chromatic number of Pn. In this paper we show that ac′(Pn) ≤ (n-2)(n-3)/2−[n/2]− ⎣10/n⎦+7 if n is even positive integer and n ≥ 10, and ac′(Pn) ≤ (n-2)(n-3)/2−[(n−1)/2] −⎣13/n⎦+8 if n is odd positive integer and n ≥ 13. For all even positive integers n ≥ 10 and all odd positive integers n ≥ 13, these results improve the upper bounds for nearly antipodal chromatic number of Pn.

Keywords: radio colorings, nearly antipodal chromatic number, paths.

2000 Mathematics Subject Classification: 05C12, 05C15, 05C78.

References

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Received 21 February 2006
Revised 31 October 2006