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Improved upper bounds for nearly antipodal chromatic number of paths

Yu-Fa Shen, Guo-Ping Zheng, Wen-Jie HeK (2007)

Discussiones Mathematicae Graph Theory

For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that a c ' ( P ) n - 2 2 + 2 for every positive integer n, where ac’(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that a c ' ( P ) n - 2 2 - n / 2 - 10 / n + 7 if n is even positive integer and n ≥ 10, and a c ' ( P ) n - 2 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.

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