Circuits and Circulant Minors

Abstract

Circulant contraction minors play a key role for characterizing ideal circular matrices in terms of minimally non ideal structures. In this article we prove necessary and sufficient conditions for a circular matrix A to have circulant contraction minors in terms of circuits in a digraph associated with A. In the particular case when A itself is a circulant matrix, our result provides an alternative characterization to the one previously known from the literature.