Abstract
We give two new algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Deng, X., Hell, P., Huang, J.: Linear-time representation algorithms for proper circular-arc graphs and proper interval graphs. SIAM J. Comput. 25(2), 390–403 (1996)
Durán, G., Gravano, A., McConnell, R.M., Spinrad, J.P., Tucker, A.: Polynomial time recognition of unit circular-arc graphs. J. Algorithms 58(1), 67–78 (2006)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)
Hell, P., Huang, J.: Certifying LexBFS recognition algorithms for proper interval graphs and proper interval bigraphs. SIAM J. Discrete Math. 18(3), 554–570 (2004)
Hell, P., Huang, J.: Interval bigraphs and circular arc graphs. J. Graph Theory 46(4), 313–327 (2004)
Kaplan, H., Nussbaum, Y.: A simpler linear-time recognition of circular-arc graphs. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 41–52. Springer, Heidelberg (2006)
Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithms for recognizing interval graphs and permutation graphs. SIAM J. Comput. 36(2), 326–353 (2006)
Lin, M.C., Szwarcfiter, J.L.: Efficient construction of unit circular-arc models. In: SODA 2006: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pp. 309–315 (2006)
McConnell, R.M.: Linear-time recognition of circular-arc graphs. Algorithmica 37(2), 93–147 (2003)
McConnell, R.M.: A certifying algorithm for the consecutive-ones property. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 768–777 (2004)
Mehlhorn, K., Näeher, S.: The LEDA Platform for combinatorial and geometric computing. Cambridge University Press, Cambridge (1999)
Meister, D.: Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs. Discrete Applied Math. 146(3), 193–218 (2005)
Skrien, D.J.: A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs. J. Graph Theory 6, 309–316 (1982)
Spinrad, J.P.: Efficient Graph Representations. Fields Institute Monographs, vol. 19. American Mathematical Society (2003)
Tarjan, R.E., Yannakakis, M.: Addendum: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 14(1), 254–255 (1985)
Tucker, A.: Matrix characterizations of circular-arc graphs. Pacific J. Math. 39(2), 535–545 (1971)
Tucker, A.: Structure theorems for some classes of circular-arc graphs. Discrete Math. 7, 167–195 (1974)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaplan, H., Nussbaum, Y. (2006). Certifying Algorithms for Recognizing Proper Circular-Arc Graphs and Unit Circular-Arc Graphs. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_26
Download citation
DOI: https://doi.org/10.1007/11917496_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48381-6
Online ISBN: 978-3-540-48382-3
eBook Packages: Computer ScienceComputer Science (R0)