Partial Characterizations of circle graphs

FLAVIA BONOMO; GUILLERMO ALFREDO DURÁN; LUCIANO NORBERTO GRIPPO; MARTÍN DARÍO SAFE

DISCRETE APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Año: 2010 vol. 159 p. 1699 - 1706

0166-218X

  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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. 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.