Geodesic
The achromatic number of the Cartesian product of $K_6$ and $K_q$
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 411-433

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 if for any pair of distinct colours c_1,c_2∈ C one can find an edge {v_1,v_2}∈ E(G) such that f(v_i)=c_i, i=1,2. The achromatic number of G is defined to be the maximum number achr(G) of colours in a proper complete vertex colouring of G. In the paper achr(K_6□ K_q) is determined for any integer q such that either 8≤ q≤40 or q≥42 is even.
Keywords: complete vertex colouring, achromatic number, Cartesian product, complete graph 
@article{DMGT_2024_44_2_a0,
     author = {Hor\v{n}\'ak, Mirko},
     title = {The achromatic number of the {Cartesian} product of $K_6$ and $K_q$},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {411--433},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a0/}
}
TY  - JOUR
AU  - Horňák, Mirko
TI  - The achromatic number of the Cartesian product of $K_6$ and $K_q$
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2024
SP  - 411
EP  - 433
VL  - 44
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a0/
LA  - en
ID  - DMGT_2024_44_2_a0
ER  - 
%0 Journal Article
%A Horňák, Mirko
%T The achromatic number of the Cartesian product of $K_6$ and $K_q$
%J Discussiones Mathematicae. Graph Theory
%D 2024
%P 411-433
%V 44
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a0/
%G en
%F DMGT_2024_44_2_a0
Horňák, Mirko. The achromatic number of the Cartesian product of $K_6$ and $K_q$. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 411-433. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a0/