Unimodularity and circle graphs

Abstract

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 [8]. In a further paper we shall interprete this result in terms of symmetric matroids introduced in [2]. In this communication we give a direct proof by means of techniques used in [1] for an algorithmic solution of the Gauss problem on self-intersecting surves in the plane.