Unimodularity and circle graphs (Q1104337)

A property of unimodularity is introduced for antisymmetric integral matrices. It is satisfied by the adjacency matrix of a circle graph provided with a Naji orientation [\textit{W. Naji}, Discrete Math. 54, 329- 337 (1985; Zbl 0567.05033)]. In a further paper we shall interprete this result in terms of symmetric matroids introduced in the author's paper in Math. Program. 38, 147-159 (1987; Zbl 0633.90089). In this communication we give a direct proof by means of techniques used in the author's paper in C. R. Acad. Sci., Paris, Ser. A 274, 724-727 (1972; Zbl 0228.05104), for an algorithmic solution of the Gauss problem on self-intersecting curves in the plane.