Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine wether a BMG can be explained by a fully resolved gene tree and, if so, to construct such a tree. Moreover, we show that all such binary trees are refinements of the unique binary-resolvable tree (BRT), which in general is a substantial refinement of the also unique least resolved tree of a BMG  .
Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine whether a BMG is binary-explainable, i.e., whether it can be explained by a fully resolved gene tree and, if so, to construct such a tree. Moreover, we show that all such binary trees are refinements of the unique binary-resolvable tree (BRT), which in general is a substantial refinement of the also unique least resolved tree of a BMG . Finally, we show that the problem of editing an arbitrary vertex-colored graph to a binary-explainable BMG is NP-complete and provide an integer linear program formulation for this task .
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wether a BMG
whether a BMG is binary-explainable, i.e., whether it
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. Finally, we show that the problem of editing an arbitrary vertex-colored graph to a binary-explainable BMG is NP-complete and provide an integer linear program formulation for this task