Isomorphism of graph classes related to the circular-ones property

Andrew R. Curtis (1) , Min Chih Lin (2) , Ross M. Mcconnell (3) , Yahav Nussbaum (4) , Francisco Juan Soulignac (2) , Jeremy P. Spinrad (5) , Jayme Luiz Szwarcfiter (6)

1 David R. Cheriton School of Computer Science
2 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
3 Computer Science Department, Colorado State University
4 TAU-CS - School of Computer Science
5 Department of Electrical Engineering & Computer Science [Nashville]
6 IM / UFRJ - Instituto de Matemática da Universidade Federal do Rio de Janeiro

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, Γ circular-arc graphs, proper circular-arc graphs and convex-round graphs.

Domaines: Mathématique discrète [cs.DM]

Andrew R. Curtis, Min Chih Lin, Ross M. Mcconnell, Yahav Nussbaum, Francisco Juan Soulignac, et al.. Isomorphism of graph classes related to the circular-ones property. Discrete Mathematics and Theoretical Computer Science, 2013, Vol. 15 no. 1 (1), pp.157--182. ⟨10.46298/dmtcs.625⟩. ⟨hal-00990614⟩