An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
On the structure of local tournaments
Journal of Combinatorial Theory Series B
Simple linear time recognition of unit interval graphs
Information Processing Letters
Recognizing interval digraphs and interval bigraphs in polynomial time
Discrete Applied Mathematics
Consecutive retrieval property-revisited
Information Processing Letters
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
A Fully Dynamic Algorithm for Recognizing and Representing Proper Interval Graphs
SIAM Journal on Computing
Minimal Representation of Semiorders with Intervals of Same Length
ORDAL '94 Proceedings of the International Workshop on Orders, Algorithms, and Applications
Restricted circular-arc graphs and clique cycles
Discrete Mathematics
Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs
SIAM Journal on Computing
Unit Circular-Arc Graph Representations and Feasible Circulations
SIAM Journal on Discrete Mathematics
Interval bigraphs and circular arc graphs
Journal of Graph 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
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs
Discrete Applied Mathematics
Fully Dynamic Representations of Interval Graphs
Graph-Theoretic Concepts in Computer Science
Journal of Computer and System Sciences
Proper Helly circular-arc graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
The clique operator on circular-arc graphs
Discrete Applied Mathematics
Characterizations and linear time recognition of helly circular-arc graphs
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Boxicity of Circular Arc Graphs
Graphs and Combinatorics
Hi-index | 0.04 |
A Helly circular-arc model M=(C,A) is a circle C together with a Helly family A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how these classes of graphs relate with straight and round digraphs.