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

LUCIANO NORBERTO GRIPPO; YIXIN CAO; MARTÍN DARÍO SAFE

DISCRETE APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2017 vol. 216 p. 67 - 83

0166-218X

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.