Geodesic
The achromatic number of the Cartesian product of $K_6$ and $K_q$
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 411-433 Cet article a éte moissonné depuis la source Library of Science

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Let G be a graph and C a finite set of colours. A vertex colouring f:V(G)→ C is complete if for any pair of distinct colours c_1,c_2∈ C one can find an edge {v_1,v_2}∈ E(G) such that f(v_i)=c_i, i=1,2. The achromatic number of G is defined to be the maximum number achr(G) of colours in a proper complete vertex colouring of G. In the paper achr(K_6□ K_q) is determined for any integer q such that either 8≤ q≤40 or q≥42 is even.
Keywords: complete vertex colouring, achromatic number, Cartesian product, complete graph 
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Horňák, Mirko. The achromatic number of the Cartesian product of $K_6$ and $K_q$. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 411-433. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a0/

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