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Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs
[chapter]
2018
2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
In this paper, we build on recent results by Chauve et al. and Bahrani and Lumbroso, which combined the splitdecomposition, 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 manageable!) set
doi:10.1137/1.9781611975062.13
dblp:conf/analco/BahraniL18
fatcat:uupao4f4yfhvfkif7fpkarb7yq