We study a new form of attractor in parity games and use it to define
solvers that run in PTIME and are partial in that they do not solve all
games completely. Technically, for color c this new attractor determines
whether player c%2 can reach a set of nodes X of color c whilst avoiding
any nodes of color less than c. Such an attractor is fatal if player c%2 can
attract all nodes in X back to X in this manner. Our partial solvers detect
fixed-points of nodes based on fatal attractors and correctly classify such
nodes as won by player c%2. Experimental results show that our partial
solvers completely solve benchmarks that were constructed to challenge
existing full solvers. Our partial solvers also have encouraging run times.
For one partial solver we prove that its runtime is in O(|V |3), that its
output game is independent of the order in which attractors are computed,
and that it solves all B¨uchi games.