2022/03/15 by Chang, Yu-Sheng, Fuchs, Michael, Liu, Hexuan +2
#05C20 #60C05 #60F05 #92D15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2203.07619
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 \it 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 \it 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.