A proof of Tutte´s realizability condition

This paper gives a simple proof of Tutte\´s realizability condition for a cutset (circuit) matrix of a nonoriented graph [1],[2]. First, a minimum nonrealizable matrix is defined as~a matrix that satisfies 1) is not a cutset (circuit) matrix, 2) does not satisfy the conditions in Tutte\´s theorem, and 3) deleting any column of or any row of any normal form of , the resultant matrix is realizable as a cutset (circuit) matrix. A proof of Tutte\´s theorem in this paper is accomplished by showing that minimum nonrealizable matrices do not exist.