Geodesic
The achromatic number of $K_6\square K_q$ equals $2q+3$ if $q\ge41$ is odd
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1103-1121

Voir la notice de l'article provenant de la source Library of Science

Let G be a graph and C a finite set of colours. A vertex colouring f:V(G)→ C is complete provided that for any two distinct colours c_1,c_2∈ C there is v_1v_2∈ E(G) such that f(v_i)=c_i, i=1,2. The achromatic number of G is the maximum number of colours in a proper complete vertex colouring of G. In the paper it is proved that if q≥41 is an odd integer, then the achromatic number of the Cartesian product of K_6 and K_q is 2q+3.
Keywords: complete vertex colouring, achromatic number, Cartesian product, complete graph 
@article{DMGT_2023_43_4_a12,
     author = {Hor\v{n}\'ak, Mirko},
     title = {The achromatic number of $K_6\square K_q$ equals $2q+3$ if $q\ge41$ is odd},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {1103--1121},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a12/}
}
TY  - JOUR
AU  - Horňák, Mirko
TI  - The achromatic number of $K_6\square K_q$ equals $2q+3$ if $q\ge41$ is odd
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2023
SP  - 1103
EP  - 1121
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a12/
LA  - en
ID  - DMGT_2023_43_4_a12
ER  - 
%0 Journal Article
%A Horňák, Mirko
%T The achromatic number of $K_6\square K_q$ equals $2q+3$ if $q\ge41$ is odd
%J Discussiones Mathematicae. Graph Theory
%D 2023
%P 1103-1121
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a12/
%G en
%F DMGT_2023_43_4_a12
Horňák, Mirko. The achromatic number of $K_6\square K_q$ equals $2q+3$ if $q\ge41$ is odd. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 1103-1121. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a12/