Isomorphism of graph classes related to the circular-ones property

Abstract

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. Our algorithm is similar to the isomorphism algorithm for interval graphs of Lueker and Booth, but works on PC trees, which are unrooted and have a cyclic nature, rather than with PQ trees, which are rooted. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, $Gamma$ circular-arc graphs, proper circular-arc graphs and convex-round graphs.Fil: Curtis, Andrew R.. University of Waterloo; CanadáFil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: McConnell, Ross M.. State University of Colorado - Fort Collins; Estados UnidosFil: Nussbaum, Yahav. Tel Aviv University; IsraelFil: Soulignac, Francisco Juan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Spinrad, Jeremy P.. Vanderbilt University; Estados UnidosFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasi