论文标题
在Rall的$ 1/2 $ - 注射统治游戏中
On Rall's $1/2$-conjecture on the domination game
论文作者
论文摘要
统治游戏上的$ 1/2 $ - 注射器断言，如果$ g $是可追溯的图，那么游戏支配数字$γ_g（g）$ g $的$ g $最多是$ \ weft \ lceil \ lceil \ frac {n（g）} {2} {2} {2} \ right \ right \ rceil $。如果$ 1/2 $ -GRAPH为$γ_g（g）= \ left \ lceil \ frac {n（g）} {2} {2} \ right \ rceil $ holds，则可追溯图是$ 1/2 $ -Graph。事实证明，所谓的挂载周期为$ 1/2 $ - 绘图，并且独一图形满足了$ 1/2 $ - 注射器。确定了支持猜想的几个其他图形系族，并与所描述的猜想相关的计算机实验。
The $1/2$-conjecture on the domination game asserts that if $G$ is a traceable graph, then the game domination number $γ_g(G)$ of $G$ is at most $\left\lceil \frac{n(G)}{2} \right\rceil$. A traceable graph is a $1/2$-graph if $γ_g(G) = \left\lceil \frac{n(G)}{2} \right\rceil$ holds. It is proved that the so-called hatted cycles are $1/2$-graphs and that unicyclic graphs fulfill the $1/2$-conjecture. Several additional families of graphs that support the conjecture are determined and computer experiments related to the conjecture described.
