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Achromatic number of $K_{5} \times K_{n}$ for small $n$

Mirko Horňák; Štefan Pčola — 2003

Czechoslovak Mathematical Journal

The achromatic number of a graph $G$ is the maximum number of colours in a proper vertex colouring of $G$ such that for any two distinct colours there is an edge of $G$ incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of $K_{5}$ and $K_{n}$ for all $n \leq 24$ .

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Achromatic number of K 5 × K n for small n

Achromatic number of $K_{5} \times K_{n}$ for small $n$