Geodesic
The application of the methods of the theory of logical derivation to graph theory
Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 781-790.

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We give an inductive definition of the property "a graph which cannot be colored with $n$ colors." 
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     title = {The application of the methods of the theory of logical derivation to graph theory},
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Yu. V. Matiyasevich. The application of the methods of the theory of logical derivation to graph theory. Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 781-790. http://geodesic.mathdoc.fr/item/MZM_1972_12_6_a15/