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Nearly antipodal chromatc number of even paths. (English) Zbl 1265.05247

Summary: For paths \(P_n\), G. Chartrand, L. Nebeský and P. Zhang [Discuss. Math., Graph Theory 24, No. 1, 5–21 (2004; Zbl 1056.05053)] 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 \(n \geq 8\).

MSC:

05C15 Coloring of graphs and hypergraphs

Citations:

Zbl 1056.05053
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