Note on Antipodal (Hamiltonian) Chromatic Number of Paths

For paths P-n, Khennoufa and Togni gave that ac(P-n) = 2p(2) - 2p + 3 if n = 2p + 1, and ac(P-n) = 2p(2) - 4p+5 if n = 2p, which disproved a conjecture posed by Chartrand, Erwin and Zhang, for antipodal chromatic number of Pn for all integer n >= 7. In this paper, by an in-depth analysis, we show that the result of Khennoufa and Togni is true, but their proof for the case n = 2p is not correct, and present a corrective proof for the result ac(P-n) = 2p(2) - 4p + 5 if n = 2p. As the hamiltonian chromatic number of P-n is equal to ac(P-n), the result of this paper also gives the exact value of hamiltonian chromatic number of P-n.