Phylogenetic analysis is a branch of biology that establishes the
evolutionary relationships between living organisms. The goal of
phylogenetic analysis is to determine the order and approximate timing
of speciation events in the evolution of a given set of species.
Phylogenetic networks allow to represent evolutionary histories that
include events like recombination and hybridization. In this paper,
we introduce a class of phylogenetic networks called extended
galled-trees in which recombination cycles share no edge. We show
that the site consistency problem, which is NP-hard in general, can be
solved in polynomial time for this class of phylogenetic networks.