Improved upper bounds for nearly antipodal chromatic number of paths

Yu-Fa Shen, Guo-Ping Zheng, and Wen-Jie HeK. "Improved upper bounds for nearly antipodal chromatic number of paths." Discussiones Mathematicae Graph Theory 27.1 (2007): 159-174. <http://eudml.org/doc/270297>.

@article{Yu2007,
abstract = {For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that $ac^\{\prime \}(Pₙ) ≤ \binom\{n-2\}\{2\} + 2$ for every positive integer n, where ac’(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that $ac^\{\prime \}(Pₙ) ≤ \binom\{n-2\}\{2\} - n/2 - ⎣10/n⎦ + 7$ if n is even positive integer and n ≥ 10, and $ac^\{\prime \}(Pₙ) ≤ \binom\{n-2\}\{2\} - (n-1)/2 - ⎣13/n⎦ + 8$ 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.},
author = {Yu-Fa Shen, Guo-Ping Zheng, Wen-Jie HeK},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {radio colorings; nearly antipodal chromatic number; paths; bounds},
language = {eng},
number = {1},
pages = {159-174},
title = {Improved upper bounds for nearly antipodal chromatic number of paths},
url = {http://eudml.org/doc/270297},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Yu-Fa Shen
AU - Guo-Ping Zheng
AU - Wen-Jie HeK
TI - Improved upper bounds for nearly antipodal chromatic number of paths
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 1
SP - 159
EP - 174
AB - For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that $ac^{\prime }(Pₙ) ≤ \binom{n-2}{2} + 2$ for every positive integer n, where ac’(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that $ac^{\prime }(Pₙ) ≤ \binom{n-2}{2} - n/2 - ⎣10/n⎦ + 7$ if n is even positive integer and n ≥ 10, and $ac^{\prime }(Pₙ) ≤ \binom{n-2}{2} - (n-1)/2 - ⎣13/n⎦ + 8$ 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.
LA - eng
KW - radio colorings; nearly antipodal chromatic number; paths; bounds
UR - http://eudml.org/doc/270297
ER -