TY  - JOUR
ID  - Horňák2021
LB  - Horňák2021
AU  - Horňák, Mirko
TI  - The achromatic number of K<sub>6</sub> □ K<sub>7</sub> is 18
ST  - The achromatic number of K<sub>6</sub> □ K<sub>7</sub> is 18
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 2
SP  - 163
EP  - 185
DO  - https://doi.org/10.7494/OpMath.2021.41.2.163
UR  - https://doi.org/10.7494/OpMath.2021.41.2.163
AB  - 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 \(\text{achr}(K_6 \square K_q)\).
KW  - complete vertex colouring
KW  - achromatic number
KW  - Cartesian product
SN  - 1232-9274
ER  -