Graph classes: a survey
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
Linear-Time Recognition of Circular-Arc Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A certifying algorithm for the consecutive-ones property
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Efficient construction of unit circular-arc models
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A simpler linear-time recognition of circular-arc graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
From a Circular-Arc Model to a Proper Circular-Arc Model
Graph-Theoretic Concepts in Computer Science
The clique operator on circular-arc graphs
Discrete Applied Mathematics
Computer Science Review
Normal Helly circular-arc graphs and its subclasses
Discrete Applied Mathematics
Structural results on circular-arc graphs and circle graphs: A survey and the main open problems
Discrete Applied Mathematics
Hi-index | 0.00 |
A circular-arc model M=(C,A) is a circle C together with a collection A of arcs of C. If no arc is contained in any other then M is a proper circular-arc model, if every arc has the same length then M is a unit circular-arc model and if A satisfies the Helly Property then M is a Helly circular-arc model. A (proper) (unit) (Helly) circular-arc graph is the intersection graph of the arcs of a (proper) (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear time recognition algorithms have been described both for the general class and for some of its subclasses. In this article we study the circular-arc graphs which admit a model which is simultaneously proper and Helly. We describe characterizations for this class, including one by forbidden induced subgraphs. These characterizations lead to linear time certifying algorithms for recognizing such graphs. Furthermore, we extend the results to graphs which admit a model which is simultaneously unit and Helly, also leading to characterizations and a linear time certifying algorithm.