A simple linear time certifying LBFS-based algorithm for recognizing trivially perfect graphs and their complements

Authors:
Frank Pok Man Chu
Affiliations:
Department of Computer Science, University of Toronto, 10 King's College Road, Toronto, ON, M5S 3G4, Canada
Venue:
Information Processing Letters
Year:
2008

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Abstract

We introduce a simple, linear time algorithm for recognizing trivially perfect (TP) graphs. It improves upon the algorithm of Yan et al. [J.-H. Yan, J.-J. Chen, G.J. Chang, Quasi-threshold graphs, Discrete Appl. Math. 69 (3) (1996) 247-255] in that it is certifying, producing a P"4 or a C"4 when the graph is not TP. In addition, our algorithm can be easily modified to recognize the complement of TP graphs (co-TP) in linear time as well. It is based on lexicographic BFS, and in particular the technique of partition refinement, which has been used in the recognition of many other graph classes [D.G. Corneil, Lexicographic breadth first search-a survey, in: WG 2004, in: Lecture Notes in Comput. Sci., vol. 3353, Springer, 2004, pp. 1-19].