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Galled-trees are a special class of graphical representation of evolutionary history that has proven amenable to efficient, polynomial-time algorithms. The goal of this paper is to construct a concise necessary and sufficient condition for the existence of a galled-tree for M, a set of binary sequences that purportedly have evolved in the presence of recombination. Both root-known and root-unknown cases are considered here.
Galled-trees, recombination, quadpartition, incompatibility.

Y. S. Song, "A Concise Necessary and Sufficient Condition for the Existence of a Galled-Tree," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. , pp. 186-191, 2006.
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