树木拓扑类型的数量

IF 1 2区数学 Q1 MATHEMATICS

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

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引用次数: 0

摘要

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。

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The Number of Topological Types of Trees

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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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.