论文标题
$ 1/2 $ - 注射统治游戏和无爪图
$1/2$-conjectures on the domination game and claw-free graphs
论文作者
论文摘要
令$γ_g（g）$为图$ g $的游戏主导号码。 Rall猜想如果$ g $是可追溯的图形，则$γ_g（g）\ le \ left \ lceil \ frac {1} {2} {2} n（g）\ right \ rceil $。我们的主要结果验证了线图等级的猜想。此外，在本文中，我们提出了以下猜想：如果$δ（g）\ geq 2 $，则$γ_g（g）\ leq \ left \ lest \ lceil \ frac {1} {2} {2} n（g）\ right \ rceil $。我们表明，这两个猜想对于无爪的立方图都是正确的。我们进一步证明了上限的$γ_g（g）\ le \ left \ lceil \ frac {11} {20} {20} \，n（g）\ right \ rceil $ the Off the Claw-fraw free traw fraw fraw fraw fraw traw traws traw traw traw traw traw traw traw traw traw traw traw traw temimim至少至少$ 2 $。还提供了支持新猜想和清晰度示例的计算机实验。
Let $γ_g(G)$ be the game domination number of a graph $G$. Rall conjectured that if $G$ is a traceable graph, then $γ_g(G) \le \left\lceil \frac{1}{2}n(G)\right\rceil$. Our main result verifies the conjecture over the class of line graphs. Moreover, in this paper we put forward the conjecture that if $δ(G) \geq 2$, then $γ_g(G) \leq \left\lceil \frac{1}{2}n(G) \right\rceil$. We show that both conjectures hold true for claw-free cubic graphs. We further prove the upper bound $γ_g(G) \le \left\lceil \frac{11}{20} \, n(G) \right\rceil$ over the class of claw-free graphs of minimum degree at least $2$. Computer experiments supporting the new conjecture and sharpness examples are also presented.
