✦ LIBER ✦
Circle graph obstructions under pivoting
✍ Scribed by Jim Geelen; Sang-il Oum
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 331 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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