Abstract
Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given for counting 1-galled networks, which are galled networks satisfying the condition that each reticulate node has only one leaf descendant. Since each galled network consists of a set of 1-galled networks connected together in a tree structure, an algorithm is also presented to count and enumerate galled networks.
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