Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks. In particular, one needs to distinguish different networks and determine whether one network is contained in another. In this paper, we introduce cherry-picking networks, a class of networks that can be reduced by a so-called cherry-picking sequence. We then show how to compare such networks using their sequences. We characterize reconstructible cherry-picking networks, which are the networks that are uniquely determined by the sequences that reduce them, making them distinguishable. Furthermore, we show that a cherry-picking network is contained in another cherry picking network if a sequence for the latter network reduces the former network, provided both networks can be reconstructed from their sequences in a similar way (i.e., they are in the same reconstructible class). Lastly, we show that the converse of the above statement holds for tree-child networks, thereby showing that Network Containment, the problem of checking whether a network is contained in another, can be solved by computing cherry picking sequences in linear time for tree-child networks.

系统发育网络用于表示生物学和语言学中的进化场景。为了找到最可能的方案，可能需要比较候选网络。特别是，一个人需要区分不同的网络，并确定一个网络是否包含在另一个网络中。在本文中，我们介绍了樱桃采摘网络，这是一种可以通过所谓的樱桃采摘序列来减少的网络。然后，我们演示如何使用它们的序列比较此类网络。我们描述了可重构的樱桃采摘网络，这些网络是由减少它们的序列唯一确定的网络，从而使其可区分。此外，我们表明，如果另一个樱桃采摘网络的序列减少了前一个网络，则另一个樱桃采摘网络中将包含一个樱桃采摘网络，前提是两个网络都可以按照类似的方式从其序列中重建（即它们属于同一可重建类）。最后，我们证明上述陈述的反面适用于树状子网络，从而表明网络遏制，网络是否包含在另一个检查的问题，可以通过在树-子网络线性时间计算樱桃采摘序列来解决。