Eternal vertex cover number of maximal outerplanar graphs

TL;DR

This paper presents a linear-time recursive algorithm for computing the eternal vertex cover number specifically for maximal outerplanar graphs, a subclass of chordal graphs, addressing a previously open problem.

Contribution

It introduces the first sub-quadratic, linear-time algorithm for this problem on maximal outerplanar graphs, expanding computational methods for this graph class.

Findings

Linear-time recursive algorithm developed

Efficient computation for maximal outerplanar graphs

Addresses open complexity question for this class

Abstract

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.