Structural results on circular-arc graphs and circle graphs: A survey and the main open problems

Authors:
Guillermo Durán;Luciano N. Grippo;Martín D. Safe
Affiliations:
CONICET, Argentina and Departamento de Matemática and Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina and Departament ...;Instituto de Ciencias, Universidad Nacional de General Sarmiento, Los Polvorines, Argentina;Instituto de Ciencias, Universidad Nacional de General Sarmiento, Los Polvorines, Argentina
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are the intersection graphs of chords on a circle. These graph classes have been the subject of much study for many years and numerous interesting results have been reported. Many subclasses of both circular-arc graphs and circle graphs have been defined and different characterizations formulated. In this survey, we summarize the most important structural results related to circular-arc graphs and circle graphs and present the main open problems.