A new lower bound for eternal vertex cover number

TL;DR

This paper introduces a novel lower bound for the eternal vertex cover number of graphs, linking it to minimum vertex covers containing cut vertices, and provides an efficient algorithm for chordal graphs.

Contribution

It presents a new lower bound for the eternal vertex cover number based on specific vertex covers and offers a quadratic time algorithm for chordal graphs.

Findings

New lower bound for eternal vertex cover number

Quadratic time algorithm for chordal graphs

Enhanced understanding of vertex cover properties

Abstract

We obtain a new lower bound for the eternal vertex cover number of an arbitrary graph $G$, in terms of the cardinality of a vertex cover of minimum size in $G$ containing all its cut vertices. The consequences of the lower bound includes a quadratic time algorithm for computing the eternal vertex cover number of chordal graphs.