Counting complete matchings without using Pfaffians

N.G. de Bruijn
1980 Indagationes Mathematicae (Proceedings)  
It is known that the number of complete matchings of a planar graph can be expressed as a Pfaffian, and that the square of the Pfaffian of a matrix equals the determinant. In this paper it is shown without the use of Pfaffians that the square of the number of complete matchings equals that determinant.
doi:10.1016/1385-7258(80)90037-2 fatcat:kkswzuv4e5eezkcvquugqikjuq