Fully-Dynamic Recognition Algorithm and Certificate for Directed Cographs.

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. [ABSTRACT FROM AUTHOR]