The achromatic number of k6 □ k7 is 18

A vertex colouring ƒ: V(G) ⇾ C of a graph G is complete if for any two distinct colours c 1 ,c2 ∈ C there is an edge {v 1 ,v2} ∈ E(G) such that ƒ (vi) = ci, i = 1, 2. The achromatic number of G is the maximum number achr(G) of colours in a proper complete vertex colouring of G. In the paper it is proved that achr(K6 □ K7) = 18. This result finalises the determination of achr(K6 □ Kq).

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).