Nearly Antipodal Chromatic Number of Even Paths

Abstract

For paths $P_n$, Chartrand, Nebesky and Zhang gave the exact value of $a{c}^{\prime }(P_n)$ for $n\le 8$, and showed that $a{c}^{\prime }(P_n)\le (\genfrac{}{}{0ex}{}{n-2}{2})+2$ for every positive integer $n$, where $a{c}^{\prime }(P_n)$ denotes the nearly antipodal chromatic number of $P_n$. In this paper, we determine the exact values of $a{c}^{\prime }(P_n)$ for all even integers $n\ge 8$.