An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
$O(M.N)$ Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs
SIAM Journal on Computing
A Linear Algorithm for Maximum Weight Cliques in ProperCircular Arc Graphs
SIAM Journal on Discrete Mathematics
Graph classes: a survey
The ultimate interval graph recognition algorithm?
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Linear Time Algorithm for Deciding Interval Graph Isomorphism
Journal of the ACM (JACM)
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
A Simple Test for Interval Graphs
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Unit Circular-Arc Graph Representations and Feasible Circulations
SIAM Journal on Discrete Mathematics
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
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
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A circular-arc model $ {\mathcal {M}} =(C,\mathcal{A})$ is a circle Ctogether with a collection $\mathcal{A}$ of arcs of C. If no arc is contained in any other then $\mathcal{M}$ is a proper circular-arc model, and if some point of Cis not covered by any arc then ${\mathcal{M}}$ is an interval model. A (proper) (interval) circular-arc graph is the intersection graph of a (proper) (interval) 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. For the isomorphism problem, there exists a polynomial time algorithm for the general case, and a linear time algorithm for interval graphs. In this work we develop a linear time algorithm for the isomorphism problem in proper circular-arc graphs, based on uniquely encoding a proper circular-arc model. Our method relies on results about uniqueness of certain PCA models, developed by Deng, Hell and Huang in [6]. The algorithm is easy to code and uses only basic tools available in almost every programming language.