Circle graph obstructions under pivoting
Jim Geelen, Sang‐il Oum · Journal of Graph Theory · 2009
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. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 1‐11, 2009