Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 67-83 |
| Number of pages | 17 |
| Journal | Discrete Applied Mathematics |
| Volume | 216 |
| DOIs | |
| Publication status | Published - 10 Jan 2017 |
Keywords
- (minimal) forbidden induced subgraphs
- (normal, Helly, proper) circular-arc models
- (proper) interval graphs
- Certifying algorithms
- Chordal graphs
- Holes
- Linear-time
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics