基于Cherry覆盖的树型网络和Orchard网络的统一刻画
A Unifying Characterization of Tree-based Networks and Orchard Networks using Cherry Covers
摘要：
系统发生网络用于研究生物学中物种之间的进化关系。这些网络通常根据其拓扑特征进行分类，这些拓扑特征源于生物和计算动机。本文研究了两类网络：树型网络和果园网络。基于树的网络是那些可以通过在底层树的边之间插入边来获得的网络。果园网络是最近引入的树子网络类的推广。树型网络的结构特征已经被发现;果园网络的情况并非如此。在本文中，我们介绍樱桃覆盖-一个统一的表征两个网络类-在其中，我们分解成所谓的樱桃形状和网状樱桃形状的网络的边缘。我们表明，樱桃覆盖可以用来描述类的树为基础的网络，以及类的果园网络。此外，我们还将这些结果推广到非二进制网络。
英文摘要：
Phylogenetic networks are used to study evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We study two network classes in this paper: tree-based networks and orchard networks. Tree-based networks are those that can be obtained by inserting edges between the edges of an underlying tree. Orchard networks are a recently introduced generalization of the class of tree-child networks. Structural characterizations have already been discovered for tree-based networks; this is not the case for orchard networks. In this paper, we introduce cherry covers---a unifying characterization of both network classes---in which we decompose the edges of the networks into so-called cherry shapes and reticulated cherry shapes. We show that cherry covers can be used to characterize the class of tree-based networks as well as the class of orchard networks. Moreover, we also generalize these results to non-binary networks.
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