# Resolving Prime Modules: The Structure of Pseudo-cographs and Galled-Tree Explainable Graphs

@article{Hellmuth2022ResolvingPM, title={Resolving Prime Modules: The Structure of Pseudo-cographs and Galled-Tree Explainable Graphs}, author={Marc Hellmuth and Guillaume E. Scholz}, journal={ArXiv}, year={2022}, volume={abs/2211.16854} }

The modular decomposition of a graph G is a natural construction to capture key features of G in terms of a labeled tree ( T , t ) whose vertices are labeled as “series” (1), “parallel” (0) or “prime”. However, full information of G is provided by its modular decomposition tree ( T , t ) only, if G is a cograph, i.e., G does not contain prime modules. In this case, ( T , t ) explains G , i.e., { x , y } ∈ E ( G ) if and only if the lowest common ancestor lca T ( x , y ) of x and y has label “1…

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