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Circle graph obstructions under pivoting
Author(s) -
Geelen Jim,
Oum Sangil
Publication year - 2009
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20363
Subject(s) - combinatorics , corollary , circle graph , mathematics , outerplanar graph , discrete mathematics , graph , pathwidth , line graph
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