@Article{Horňák2021,
author = "Horňák, Mirko",
title = "The achromatic number of K<sub>6</sub> □ K<sub>7</sub> is 18",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "2",
pages = "163--185",
doi = "https://doi.org/10.7494/OpMath.2021.41.2.163",
url = "https://doi.org/10.7494/OpMath.2021.41.2.163",
abstract = "A vertex colouring \(f:V(G)\to C\) of a graph \(G\) is complete if for any two distinct colours \(c_1, c_2 \in C\) there is an edge \(\{v_1,v_2\}\in E(G)\) such that \(f(v_i)=c_i\), \(i=1,2\). The achromatic number of \(G\) is the maximum number \(\text{achr}(G)\) of colours in a proper complete vertex colouring of \(G\). In the paper it is proved that \(\text{achr}(K_6 \square K_7)=18\). This result finalises the determination of \(\text{achr}(K_6 \square K_q)\).",
keywords = "complete vertex colouring, achromatic number, Cartesian product",
issn = "1232-9274"
}