Stability in circular arc graphs
Journal of Algorithms
Convergence of iterated clique graphs
Discrete Mathematics
Graph classes: a survey
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
Recognizing quasi-triangulated graphs
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
The clique operator on graphs with few P4's
Discrete Applied Mathematics
Algorithms for clique-independent sets on subclasses of circular-arc graphs
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Unit Circular-Arc Graph Representations and Feasible Circulations
SIAM Journal on Discrete Mathematics
European Journal of Combinatorics
Proper Helly circular-arc graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Clique graph recognition is NP-complete
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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
Normal Helly circular-arc graphs and its subclasses
Discrete Applied Mathematics
Theoretical Computer Science
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A circular-arc graphG is the intersection graph of a collection of arcs on the circle and such a collection is called a model of G. Say that the model is proper when no arc of the collection contains another one, it is Helly when the arcs satisfy the Helly Property, while the model is proper Helly when it is simultaneously proper and Helly. A graph admitting a Helly (resp. proper Helly) model is called a Helly (resp. proper Helly) circular-arc graph. The clique graphK(G) of a graph G is the intersection graph of its cliques. The iterated clique graphK^i(G) of G is defined by K^0(G)=G and K^i^+^1(G)=K(K^i(G)). In this paper, we consider two problems on clique graphs of circular-arc graphs. The first is to characterize clique graphs of Helly circular-arc graphs and proper Helly circular-arc graphs. The second is to characterize the graph to which a general circular-arc graph K-converges, if it is K-convergent. We propose complete solutions to both problems, extending the partial results known so far. The methods lead to linear time recognition algorithms, for both problems.