Lions and contamination: Monotone clearings

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