The Number of Topological Types of Trees

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2024-04-04 DOI:10.1007/s00493-024-00087-2

引用次数: 0

Abstract

Two graphs are of the same topological type if they can be mutually embedded into each other topologically. We show that there are exactly \(\aleph _1\) distinct topological types of countable trees. In general, for any infinite cardinal \(\kappa \) there are exactly \(\kappa ^+\) distinct topological types of trees of size \(\kappa \) . This solves a problem of van der Holst from 2005.

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树木拓扑类型的数量

摘要如果两个图在拓扑上可以相互嵌入，那么它们就具有相同的拓扑类型。我们证明，可数树的拓扑类型恰好有(\aleph _1\)种不同的拓扑类型。一般来说，对于任意一个无限红心（\kappa \），大小为 \(\kappa \)的树恰好有 \(\kappa ^+\) 个不同的拓扑类型。这解决了 van der Holst 在 2005 年提出的一个问题。

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

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.