Computing eternal vertex cover number of maximal outerplanar graphs in linear time

Abstract

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