Partial Characterizations of Circle Graphs.
Flavia Bonomo, Guillermo Durán, Luciano N. Grippo, Martín D. Safe · Repositorio Digital Institucional de la Universidad de Buenos Aires (Universidad de Buenos Aires) · 2009
A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the following classes: linear domino graphs, P4-tidy graphs, and tree-cographs. We also completely characterize by minimal forbidden induced subgraphs the class of unit Helly circle graphs, which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. © 2010 Elsevier B.V. All rights reserved.