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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

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✦ 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