Geodesic
Coloring digraphs by iterated antichains
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 209-212.

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We show that the minimum chromatic number of a product of two $n$-chromatic graphs is either bounded by 9, or tends to infinity. The result is obtained by the study of coloring iterated adjoints of a digraph by iterated antichains of a poset.
Classification : 05C15, 06A06, 06A07, 06A10
Keywords: graph product; chromatic number; antichain 
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     title = {Coloring digraphs by iterated antichains},
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Poljak, Svatopluk. Coloring digraphs by iterated antichains. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 209-212. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a0/