  An independent set game is a cooperative game defined on graphs and dealing
with profit-sharing in maximum independent set problems. A population monotonic
allocation scheme is a rule specifying how to share the profit of each
coalition among its participants such that every participant is better off when
the coalition expands. In this paper, we provide a necessary and sufficient
characterization for population monotonic allocation schemes in independent set
games. Moreover, our characterization can be verified efficiently.
