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Enumeration of d-Combining Tree-Child Networks

Authors Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, Guan-Ru Yu



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Author Details

Yu-Sheng Chang
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Michael Fuchs
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Hexuan Liu
  • Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan
Michael Wallner
  • Institute of Discrete Mathematics and Geometry, TU Wien, Vienna, 1040, Austria
Guan-Ru Yu
  • Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 824, Taiwan

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Yu-Sheng Chang, Michael Fuchs, Hexuan Liu, Michael Wallner, and Guan-Ru Yu. Enumeration of d-Combining Tree-Child Networks. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 5:1-5:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.5

Abstract

Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for bicombining tree-child networks which are tree-child networks with every reticulation node having exactly two parents. In this paper, we extend these studies to d-combining tree-child networks where every reticulation node has now d ≥ 2 parents. Moreover, we also give results and conjectures on the distributional behavior of the number of reticulation nodes of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
Keywords
  • Phylogenetic network
  • tree-child network
  • d-combining tree-child network
  • exact enumeration
  • asymptotic enumeration
  • reticulation node
  • limit law
  • stretched exponential

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References

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