Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs

@inproceedings{Bahrani2018SplitDecompositionTW,
  title={Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs},
  author={Maryam Bahrani and J{\'e}r{\'e}mie O. Lumbroso},
  booktitle={ANALCO},
  year={2018}
}
In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on graphs---in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptolemaic). Our goal was to study a simple family of graphs, of which the split-decomposition trees have prime nodes drawn from an enumerable (and… 

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