Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most \(15k-9\) taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees, and that this bound is tight. Here, we propose five new reduction rules and show that these further reduce the bound to \(11k-9\). The new rules combine the “unrooted generator” approach introduced in Kelk and Linz (SIAM J Discrete Math 33(3):1556–1574, 2019) with a careful analysis of agreement forests to identify (i) situations when chains of length 3 can be further shortened without reducing the TBR distance, and (ii) situations when small subtrees can be identified whose deletion is guaranteed to reduce the TBR distance by 1. To the best of our knowledge these are the first reduction rules that strictly enhance the reductive power of the subtree and chain reduction rules.

最近的研究表明，如果将子树和链减少规则完全应用于两个无根的系统发育树，则减少的树将最多具有\（15k-9 \）分类单元，其中k是TBR（树二等分和重新连接）距离在两棵树之间，并且这个界限很紧。在这里，我们提出了五个新的归约规则，并表明它们进一步简化了\（11k-9 \）的边界。新规则结合了Kelk和Linz（SIAM J Discrete Math 33（3）：1556-1574，2019）中引入的“无根生成器”方法以及对协议林的仔细分析，以识别（i）长度为3的链可以在不减小TBR距离的情况下进一步缩短，以及（ii）可以确定可以保证删除的小子树将TBR距离减小1的情况。据我们所知，这是严格增强还原能力的第一条减少规则子树和链减少规则。