Abstract.
We provide an asymptotic formula for the number of labelled essential DAGs a n and show that lim n →∞a n ′/a n =c, where a n ′ is the number of labelled DAGs and c≈13.65, which is interesting in the field of Bayesian networks. Furthermore, we present an asymptotic formula for the number of labelled chain graphs.
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Acknowledgment. I would like to thank Prof. Peter Grabner for his support and very helpful discussions, which where constitutive for this article. I am also thankful to the referees for their comments.
This Research was supported by the Austrian Science Fund (FWF), START-Project Y96-MAT
Final version received: January 28, 2004
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Steinsky, B. Asymptotic Behaviour of the Number of Labelled Essential Acyclic Digraphs and Labelled Chain Graphs. Graphs and Combinatorics 20, 399–411 (2004). https://doi.org/10.1007/s00373-004-0569-9
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DOI: https://doi.org/10.1007/s00373-004-0569-9