Fully-Dynamic recognition algorithm and certificate for directed cographs

Authors:
Christophe Crespelle;Christophe Paul
Affiliations:
CNRS – LIRMM, Montpellier Cedex 5, France;CNRS – LIRMM, Montpellier Cedex 5, France
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

This paper presents an optimal fully-dynamic recognition algorithm for directed cographs. Given the modular decomposition tree of a directed cograph G, the algorithm supports arc and vertex modification (insertion or deletion) in $\mathcal{O}(d)$ time where d is the number of arcs involved in the operation. Moreover, if the modified graph remains a directed cograph, the modular tree decomposition is updated; otherwise, a certificate is returned within the same complexity.