Cograph generation with linear delay
\'Atila A. Jones, F\'abio Protti, Renata R. Del-Vecchio

TL;DR
This paper introduces a linear-delay algorithm for generating all unlabeled cographs with n vertices efficiently, avoiding duplicates and providing a linear ordering of the generated graphs.
Contribution
The authors present a novel algorithm that generates all unlabeled cographs with linear delay, improving efficiency and avoiding isomorphic duplicates.
Findings
Generation delay is O(n) per cograph.
Overall complexity is O(n * M_n), where M_n is the number of cographs.
Produces a linear ordering of unlabeled cographs.
Abstract
Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consecutive outputs) is . The time needed to generate the first output is also , which gives an overall time complexity, where is the number of unlabeled cographs with vertices. The algorithm avoids the generation of duplicates (isomorphic outputs) and produces, as a by-product, a linear ordering of unlabeled cographs wih vertices.
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