Reconstruction of caterpillar tanglegrams

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.dam.2025.09.022

Ann Clifton , Éva Czabarka , Kevin Liu , Sarah Loeb , Utku Okur , László Székely , Kristina Wicke

引用次数: 0

Abstract

A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. Given a size-

n

tanglegram, i.e., a tanglegram for two trees with

n

leaves, a multiset of induced size-

(n - 1)

tanglegrams is obtained by deleting a pair of matched leaves in every possible way. Here, we analyze whether a size-

n

tanglegram is uniquely encoded by this multiset of size-

(n - 1)

tanglegrams. We answer this question affirmatively in the case that at least one of the two trees of the tanglegram is a caterpillar tree.

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毛虫缠结图的重建

缠结图由两棵有根的二叉树组成，这两棵树的叶子数量相同，叶子之间完美匹配。给定一个大小为n的缠结图，即两个有n个叶子的树的缠结图，通过以各种可能的方式删除一对匹配的叶子，得到一个诱导大小为-(n−1)的缠结图的多集。在这里，我们分析了大小为n的缠结图是否被大小为-(n−1)的缠结图的多集唯一编码。如果缠结图的两棵树中至少有一棵是毛虫树，我们可以肯定地回答这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.