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A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or moreleaves share a label, e.g., a species name. A MUL-tree can imply multipleconflicting phylogenetic relationships for the same set of taxa, but can alsocontain conflict-free information that is of interest and yet is not obvious.We define the information content of a MUL-tree T as the set of allconflict-free quartet topologies implied by T, and define the maximal reducedform of T as the smallest tree that can be obtained from T by pruning leavesand contracting edges while retaining the same information content. We showthat any two MUL-trees with the same information content exhibit the samereduced form. This introduces an equivalence relation in MUL-trees withpotential applications to comparing MUL-trees. We present an efficientalgorithm to reduce a MUL-tree to its maximally reduced form and evaluate itsperformance on empirical datasets in terms of both quality of the reduced treeand the degree of data reduction achieved.

Extracting Conflict-free Information from Multi-labeled Trees