发表机构
Stockholm University; Leipzig University; University of Vienna; Max Planck Institute for Mathematics in the Sciences; Universidad Nacional de Colombia; Santa Fe Institute（斯德哥尔摩大学; 莱比锡大学; 维也纳大学; 马普科学数学研究所; 哥伦比亚国立大学; 圣塔菲研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将最佳匹配图概念从树推广到有根网络，刻画了网络BMGs的图论性质，并提出了线性时间识别与二次时间构建解释性网络的算法，同时扩展至互惠最佳匹配图。
AI 中文摘要
最佳匹配图（BMGs）在数学系统发育学中被引入，用以描述不同生物体（定义叶颜色）中相关基因（有根树的叶）的最亲近亲属概念。我们在此将该概念推广到叶着色的有根网络，其中最近共同祖先通常既不唯一也不可比。我们将有根网络的BMGs刻画为那些适当着色且满足一个易于检查的条件（我们称之为sicor-in-hub性质）的顶点着色有向图。BMGs可以在线性时间内识别，并且可以在二次时间内构建一个解释性网络。对于互惠最佳匹配图（RBMGs）也获得了类似的结果，其中边{x,y}对应于不同颜色的顶点对，它们互为最亲近亲属。
英文摘要
Best match graphs (BMGs) were introduced in mathematical phylogenetics to describe the concept of closest relatives for related genes (leaves of rooted tree) in different organisms (defining leaf colors). We generalize this concept here to leaf-colored rooted networks, where least common ancestors are in general neither unique nor comparable. We characterize BMGs of rooted networks as those vertex-colored digraphs that are properly colored and satisfy an easy-to-check condition that we call the sicor-in-hub property. BMGs can be recognized in linear time and an explaining network can be constructed in quadratic time. Analogous results are obtained for reciprocal best match graphs (RBMGs), where an edge $\{x,y\}$ corresponds to pairs of vertices with different color that are mutually closest relatives.
