superglue | SuperGlue -- A C Library for Data-Dependency Driven Task | Job Scheduling library

You are given an n x n chessboard with k knights (of the same color) on it. Someone has spilled superglue on k of the squares, and if a knight ever finishes his move on one of these glue squares, it becomes stuck forever. Additionally (and this is why we can't have nice things) someone has cut out some of the squares so the chessboard has holes in it. You are given an initial position of the knights. The knights move as they do in regular chess, but unlike regular chess, on each turn all the knights move at once (except of course the stuck ones). At the end of each move, a square cannot be occupied by more than 1 knight. Hole squares can't be occupied by knights either (but they do count as squares that the knight can jump over). Give an 0(t x poly(n))-time algorithm to determine whether you can use < t moves to move all the knights from their initial positions to new positions where they are each stuck at a glue square.

My initial thought is to formulate this problem into a maximum flow problem and use Ford-Fulkerson algorithm to solve it. But I am not sure what my nodes and edges should be. Any idea? Thanks!