Lions and contamination: Monotone clearings

Abstract

We consider a special variant of a pursuit-evasion game called lions and contamination. In a graph whose vertices are originally contaminated, a set of lions walks around the graph and each lion clears the contamination from every vertex it visits. The contamination, however, simultaneously spreads to any adjacent vertex not occupied by a lion. We study the relationship between different types of clearings of graphs, such as clearings which do not allow recontamination, clearings where at most one lion moves at each time step and clearings where lions are forbidden to be stacked on the same vertex. We answer several questions raised by Adams et al. [1].