Forbidden induced subgraphs of normal Helly circular-arc graphs : characterization and detection

• Autores: Cao, Yixin; Grippo, Luciano Norberto; Safe, Martín D.
• Año de publicación: 2017
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Applied Mathematics. 2017; (216): 67-83
• Materia: Certifying algorithms; Linear-time; (Proper) Interval graphs; Chordal graphs; (Minimal) Forbidden Induced Subgraphs; Holes; (Normal, Helly, proper) Circular-arc Models
• Institución: Universidad Nacional de General Sarmiento

Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Safe, Martín D. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Cao, Yixin. Hong Kong Polytechnic University. Department of Computing; China.
A normal Helly circular-arc graph is the intersection graph of a set of arcs on a circle of which no three or less arcs cover the whole circle. Lin et al. (2013) characterized circular-arc graphs that are not normal Helly circular-arc graphs, and used them to develop the first recognition algorithm for this graph class. As open problems, they ask for the forbidden subgraph characterization and a direct recognition algorithm for normal Helly circular-arc graphs, both of which are resolved by the current paper. Moreover, when the input is not a normal Helly circular-arc graph, our recognition algorithm finds in linear time a minimal forbidden induced subgraph as a certificate. Our approach yields also a considerably simpler algorithm for the certifying recognition of proper Helly circular-arc graphs, a subclass of normal Helly circular-arc graphs.