Nearly Antipodal Chromatic Number of Even Paths

Abstract

For paths \(P_n\), Chartrand, Nebesky and Zhang gave the exact value of \(ac'(P_n)\) for \(n \leq 8\), and showed that \(ac'(P_n) \leq \binom{n-2}{2}+2\) for every positive integer \(n\), where \(ac'(P_n)\) denotes the nearly antipodal chromatic number of \(P_n\). In this paper, we determine the exact values of \(ac'(P_n)\) for all even integers \(n \geq 8\).