# Structural characterization of some problems on circle and interval graphs

@article{Pardal2020StructuralCO, title={Structural characterization of some problems on circle and interval graphs}, author={Nina Pardal}, journal={ArXiv}, year={2020}, volume={abs/2006.00099} }

A graph is circle if there is a family of chords in a circle such that two vertices are adjacent if the corresponding chords cross each other. There are diverse characterizations of circle graphs, many of them using the notions of local complementation or split decomposition. However, there are no known structural characterization by minimal forbidden induced subgraphs for circle graphs. In this thesis, we give a characterization by forbidden induced subgraphs of circle graphs within split…

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## 2 Citations

Forbidden induced subgraph characterization of circle graphs within split graphs

- MathematicsArXiv
- 2020

2-nested Matrices: towards Understanding the Structure of Circle Graphs

- MathematicsGraphs and Combinatorics
- 2022

2-nested matrices are defined and characterised, which are (0, 1)matrices with a variant of the C1P and for which there is also certain assignment of one of two colors to each block of consecutive 1’s in each row.

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