Counting Cherry Reduction Sequences in Phylogenetic Tree-Child Networks is Counting Linear Extensions

Abstract

[eng] Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries andreticulated cherries. As it is the case with phylogenetic trees, the number of ways inwhich this can be done gives information about the topology of the network. Here, we show that the problem of computing this number in tree-child networks is akin to that of finding the number of linear extensions of the poset induced by each network, and give an algorithm based on this reduction whose complexity is bounded in terms of the level of the network.