SWAT 2008: Algorithm Theory – SWAT 2008 pp 355-366

# A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs

• Min Chih Lin
• Francisco J. Soulignac
• Jayme L. Szwarcfiter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)

## Abstract

A circular-arc model $${\mathcal {M}} =(C,\mathcal{A})$$ is a circle C together 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 C is 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.

## Keywords

isomorphism problems proper circular-arc graphs proper circular-arc canonization

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## Authors and Affiliations

• Min Chih Lin
• 1
• Francisco J. Soulignac
• 1
• Jayme L. Szwarcfiter
• 2
1. 1.Facultad de Ciencias Exactas y Naturales, Departamento de ComputaciónUniversidad de Buenos AiresBuenos AiresArgentina
2. 2.Instituto de Matemática, NCE and COPPEUniversidade Federal do Rio de JaneiroRio de JaneiroBrasil