利用图的割刻画无根树的相容性和一致性
Characterizing Compatibility and Agreement of Unrooted Trees via Cuts in Graphs
摘要：
决定是否有一个单一的树-一个超级树-总结了一系列无根树的进化信息是遗传学中的一个基本问题。我们考虑这个问题的两个版本：一致性和兼容性。在第一种情况下，超树需要精确地反映输入树所表现出的物种之间的关系。在第二种情况下，超树可以比输入树更精细。树的兼容性可以用一种特定的三角剖分在一个被称为显示图的结构中的存在来表征。或者，它可以被描述为一个弦图三明治问题的结构称为边标签相交图。在这里，我们表明，后者的表征产生一个自然的表征的兼容性方面的最小切割显示图，这是密切相关的分裂的兼容性。然后，我们得到一个表征协议。
英文摘要：
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and compatibility. In the first, the supertree is required to reflect precisely the relationships among the species exhibited by the input trees. In the second, the supertree can be more refined than the input trees. Tree compatibility can be characterized in terms of the existence of a specific kind of triangulation in a structure known as the display graph. Alternatively, it can be characterized as a chordal graph sandwich problem in a structure known as the edge label intersection graph. Here, we show that the latter characterization yields a natural characterization of compatibility in terms of minimal cuts in the display graph, which is closely related to compatibility of splits. We then derive a characterization for agreement.
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