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Topological ubiquity of trees

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Title
Topological ubiquity of trees
Author(s)
Bowler, Nathan; Elbracht, Christian; Erde, Joshua; J. Pascal Gollin; Heuer, Karl; Pitz, Max; Teegen, Maximilian
Publication Date
2022-11
Journal
Journal of Combinatorial Theory. Series B, v.157, pp.70 - 95
Publisher
Academic Press Inc.
Abstract
Let ⊲ be a relation between graphs. We say a graph G is ⊲-ubiquitous if whenever Γ is a graph with nG⊲Γ for all n∈N, then one also has ℵ0G⊲Γ, where αG is the disjoint union of α many copies of G. The Ubiquity Conjecture of Andreae, a well-known open problem in the theory of infinite graphs, asserts that every locally finite connected graph is ubiquitous with respect to the minor relation. In this paper we show that all trees are ubiquitous with respect to the topological minor relation, irrespective of their cardinality. This answers a question of Andreae from 1979.
URI
https://pr.ibs.re.kr/handle/8788114/12362
DOI
10.1016/j.jctb.2022.05.011
ISSN
0095-8956
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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