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Improved upper bounds for nearly antipodal chromatic number of paths

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Shen Y.-F., Zheng G.-P., He W.-J.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

159-174

For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that $ac'(Pₙ) ≤ \binom{n-2}{2} + 2$ for every positive integer n, where ac'(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that $ac'(Pₙ) ≤ \binom{n-2}{2} - n/2 - ⎣10/n⎦ + 7$ if n is even positive integer and n ≥ 10, and $ac'(Pₙ) ≤ \binom{n-2}{2} - (n-1)/2 - ⎣13/n⎦ + 8$ 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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 He W.-J.

1 Shen Y.-F.

1 Zheng G.-P.

1 2007

Wyniki wyszukiwania

Improved upper bounds for nearly antipodal chromatic number of paths