We study a discrete diffusion process introduced in some combinatorial puzzles called Flood-It, Mad Virus, or Honey-Bee, that can be played online and whose computational complexities have recently been studied. Originally defined on regular boards, we show that studying their dynamics directly on general graphs is valuable: we synthesize and extend previous results, we show how to solve Flood-It on cycles by computing a poset height and how to solve the 2-Free-Flood-It variant by computing a graph radius.
