Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of the problem for bipartite graphs is open. There is a quadratic complexity algorithm known for this problem for chordal graphs. Maximal outerplanar graphs forms a subclass of chordal graphs, for which no algorithm of sub-quadratic time complexity is known. In this paper, we obtain a recursive algorithm of linear time for computing eternal vertex cover number of maximal outerplanar graphs.

翻译：Eternal 顶点覆盖问题是古典顶点覆盖问题的一种变体,它以两个玩家攻击者- defender 游戏为模型模型。 计算永久顶点覆盖图数一般已知为NP- 硬度, 双边图形问题的复杂性状态是开放的。 在这个 cordal 图形的问题中, 存在着一种已知的二次复杂算法。 最大外平面图形形成一个相形图的子类, 而对于它来说, 不存在次赤道时间复杂性的算法 。 在本文中, 我们获得了计算永久顶点外平面图形覆盖数的线性时间递归算法 。