Forbidden Induced Subgraphs of Normal Helly Circular-Arc Graphs: Characterization and Detection
Abstract
A normal Helly circular-arc graph is the intersection graph of arcs on a circle of which no three or less arcs cover the whole circle. Lin, Soulignac, and Szwarcfiter [Discrete Appl. Math. 2013] characterized circular-arc graphs that are not normal Helly circular-arc graphs, and used it to develop the first recognition algorithm for this graph class. As open problems, they ask for the forbidden induced 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 certificate.
Keywords
Cite
@article{arxiv.1405.0329,
title = {Forbidden Induced Subgraphs of Normal Helly Circular-Arc Graphs: Characterization and Detection},
author = {Yixin Cao and Luciano N. Grippo and Martín D. Safe},
journal= {arXiv preprint arXiv:1405.0329},
year = {2014}
}
Comments
Preliminary results of this paper appeared in the proceedings of SBPO 2012 and FAW 2014