论文标题
$ k_6 $和$ k_q $的笛卡尔产品的可观数量
The achromatic number of the Cartesian product of $K_6$ and $K_q$
论文作者
论文摘要
令$ g $为图表，$ c $是有限的颜色。如果对于任何一对不同的颜色$ c_1，c_2 \ in c $，一个人可以找到一个边缘$ \ {v_2 \} \ in E（g）$，这样， $ g $的可观数字定义为最大数字$ \ mathrm {achr}（g）$的颜色，在适当的完整顶点着色$ g $中。在论文中，$ \ mathrm {achr}（k_6 \ square k_q）$是针对任何整数$ q $确定的，使得$ 8 \ le q \ le40 $或$ q \ ge42 $均匀。
Let $G$ be a graph and $C$ a finite set of colours. A vertex colouring $f:V(G)\to C$ is complete if for any pair of distinct colours $c_1,c_2\in C$ one can find 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 defined to be the maximum number $\mathrm{achr}(G)$ of colours in a proper complete vertex colouring of $G$. In the paper $\mathrm{achr}(K_6\square K_q)$ is determined for any integer $q$ such that either $8\le q\le40$ or $q\ge42$ is even.
