Minimal separators in extended P4-laden graphs

Authors:
Vagner Pedrotti;CéLia Picinin De Mello
Affiliations:
Institute of Computing, University of Campinas, Campinas, Brazil and Faculty of Computing, UFMS, Campo Grande, Brazil;Institute of Computing, University of Campinas, Campinas, Brazil
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

In this paper, we use the primeval decomposition tree to compute the minimal separators of some graphs and to describe a linear-time algorithm that lists the minimal separators of extended P"4-laden graphs, extending an algorithm for P"4-sparse graphs given by Nikolopoulos and Palios [S.D. Nikolopoulos, L. Palios, Minimal separators in P"4-sparse graphs, Discrete Math. 306 (3) (2006) 381-392]. We also give bounds on the number and total size of all minimal separators of extended P"4-laden graphs and some of their subclasses, such as P"4-tidy and P"4-lite graphs. Moreover, we show that these bounds are tight for all subclasses considered.