2024/03/05 by Yu‐Sheng Chang, Chang, Yu-Sheng, Michael Fuchs +3
Agricultural and Biological Sciences · Environmental Science · #05C20 #60C05 #60F05 #92D15 #Agriculture and Rural Development Research #Combinatorics (math.CO) #FOS: Mathematics #Oil Palm Production and Sustainability #Plant and animal studies
paper · pdf · doi:10.48550/arxiv.2403.02923
openalex publication_date 2024/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been proved with very different methods. We show that a counting result for the class of galled tree-child networks follows with similar tools as used for galled networks, however, the result has a similar pattern as the one for tree-child networks. In addition, we also consider the (suitably scaled) numbers of reticulation nodes of random galled tree-child networks and show that they are asymptotically normal distributed. This is in contrast to the limit laws of the corresponding quantities for galled networks and tree-child networks which have been both shown to be discrete.