论文标题
M端支配中有效的攻击序列
Efficient attack sequences in m-eternal domination
论文作者
论文摘要
我们从攻击者的角度研究了M端的统治问题。对于许多图形类别，已知的最小必需防护卫队数量是已知的。根据定义，如果防守者的后卫人数小于所需的警卫人数，则存在一系列攻击，以确保攻击者的胜利。对于这种攻击序列，尤其是无界的长度，知之甚少。 我们表明，如果在$ n $顶点上的树$ t $上玩游戏，并且防守者的后卫人数少于必要的后卫数量，那么攻击者最多可以赢得$ n $ tho。此外，我们提出了一种有效的程序，该程序会产生这种攻击策略。
We study the m-eternal domination problem from the perspective of the attacker. For many graph classes, the minimum required number of guards to defend eternally is known. By definition, if the defender has less than the required number of guards, then there exists a sequence of attacks that ensures the attacker's victory. Little is known about such sequences of attacks, in particular, no bound on its length is known. We show that if the game is played on a tree $T$ on $n$ vertices and the defender has less than the necessary number of guards, then the attacker can win in at most $n$ turns. Furthermore, we present an efficient procedure that produces such an attacking strategy.
