论文标题
关于Viping的猜想的注释
A note on Vizing's conjecture
论文作者
论文摘要
令$γ（g）$表示图形$ g $的统治数。让$ g $和$ h $是图形和$ g \ box h $它们的笛卡尔产品。对于$ h \ in v（h）$定义$ g_h = \ {（g，h）\，| \，g \ in v（g）\} $ in v（g）\} $，并将此设置称为$ g \ box h $的$ g $ -layer。我们证明了Viping的猜想的以下特殊情况。令$ d $为$ g \ box h $的主导套装。如果最低限度的统治集$ d_1 $和$ d_2 $ $ g $，以便对于v（h）$中的每一个$ h \，$ d \ cap g_h $ to $ g $的投影包含在$ d_1 $或$ d_2 $中，则包含$ d_1 $或$ d_2 $，然后$ | d | d | d | d | \ geq feqqγ（g）γ$。
Let $γ(G)$ denote the domination number of graph $G$. Let $G$ and $H$ be graphs and $G\Box H$ their Cartesian product. For $h\in V(H)$ define $G_h=\{(g,h)\,|\,g\in V(G)\}$ and call this set a $G$-layer of $G\Box H$. We prove the following special case of Vizing's conjecture. Let $D$ be a dominating set of $G\Box H$. If there exist minimum dominating sets $D_1$ and $D_2$ of $G$ such that for every $h\in V(H)$, the projection of $D\cap G_h$ to $G$ is contained in $D_1$ or $D_2$, then $|D|\geq γ(G)γ(H)$.
