Geodesic
Oriented Chromatic Number of Cartesian Products $ P_m \square P_n $ and $ C_m \square P_n $
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 799-810

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We consider oriented chromatic number of Cartesian products of two paths P_m □ P_n and of Cartesian products of paths and cycles, C_m □ P_n. We say that the oriented graph G is colored by an oriented graph H if there is a homomorphism from G to H. In this paper we show that there exists an oriented tournament H_10 with ten vertices which colors every orientation of P_8 □ P_n and every orientation of C_m □ P_n, for m = 3, 4, 5, 6, 7 and n ≥ 1. We also show that there exists an oriented graph T_16 with sixteen vertices which colors every orientation of C_m □ P_n.
Keywords: graphs, oriented coloring, oriented chromatic number 
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     title = {Oriented {Chromatic} {Number} of {Cartesian} {Products} $ P_m \square P_n $ and $ C_m \square P_n $},
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Nenca, Anna. Oriented Chromatic Number of Cartesian Products $ P_m \square P_n $ and $ C_m \square P_n $. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 799-810. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a7/