随机图上的熄灯游戏
组合数学
2022-08-10 v2 概率论
摘要
我们考虑在图上进行的广义熄灯游戏，并研究以下问题：对于给定的正整数，从具有个顶点的图集合中均匀随机选取的图产生普遍可解熄灯游戏的概率是多少？当时，我们通过判定每个具有个顶点的图游戏是否普遍可解来精确计算该概率。我们对每个满足的正整数，通过应用使用1,000,000次试验的蒙特卡洛方法近似该概率。我们还对连通图执行了类似的计算。
引用
@article{arxiv.2108.07349,
title = {Lights Out On A Random Graph},
author = {Bradley Forrest and Nicole Manno},
journal= {arXiv preprint arXiv:2108.07349},
year = {2022}
}
备注
10 pages, 1 figure. The first version incorrectly stated that the number of unlabeled graphs with n vertices was known up to n=87. It is known at least up n=140, see reference 5. Consequently, we extended our results from n=87 to n=100, which required improving our algorithm. All results in the second version were obtained using the new code