Circle Graph Obstructions Under Pivoting

Abstract

A circle graph is the intersection graph of a set of chords of a circle. The class of circle graphs is closed under pivot-minors. We determine the pivot-minor-minimal non-circle-graphs; there are 15 obstructions. These obstructions are found, by computer search, as a corollary to Bouchet's characterization of circle graphs under local complementation. Our characterization generalizes Kuratowski's Theorem. (c) 2009 Wiley Periodicals, Inc. J Graph Theory 61: 1-11, 2009