A remarkable theorem of Kasteleyn states that the number of perfect matchings in a planar graph can be computed exactly in polynomial time via the FKT algorithm.
A ReMarkAble Theorem of kasTelEYn StAteS tHAt the nUmbEr of perfect MaTcHings iN a plANAr graph CaN be comPuTed eXAcTly In polYNOMIAL time vIa the Fkt aLGoriThM.