A linear Algorithm For The Eternal Feedback Vertex Set on Interval Graphs*

The Eternal Feedback Vertex Set problem is a new model of protecting graphs using mobile guards, which is usually modeled using a two-players game; a defender and an attacker. This model is based on an initial selection, by the defender, of a dominating feedback vertex set F used to hold guards, where a guard can be moved to a neighboring attacked vertex of F. The resulting guard configuration must be also a dominating feedback vertex set. In this paper, we prove that the eternal feedback vertex number F ∞ (G), which is the minimal cardinality of F , on an interval graph G depends on the number of cliques in G. Then, we develop a linear algorithm for finding the eternal feedback vertex set on G