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Ubiquity of graphs with nowhere-linear end structure

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Title
Ubiquity of graphs with nowhere-linear end structure
Author(s)
Bowler, Nathan; Elbracht, Christian; Erde, Joshua; J. Pascal Gollin; Heuer, Karl; Pitz, Max; Teegen, Maximilian
Publication Date
2023-07
Journal
JOURNAL OF GRAPH THEORY, v.103, no.3, pp.564 - 598
Publisher
WILEY
Abstract
A graph G G is said to be less than or similar to-ubiquitous, where less than or similar to is the minor relation between graphs, if whenever Gamma is a graph with Gamma for all n is an element of N, then one also has aleph(0)G less than or similar to Gamma where alpha G is the disjoint union of alpha many copies of G. A well-known conjecture of Andreae is that every locally finite connected graph is less than or similar to-ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph G which implies that G is less than or similar to-ubiquitous. In particular this implies that the full-grid is less than or similar to-ubiquitous.
URI
https://pr.ibs.re.kr/handle/8788114/13353
DOI
10.1002/jgt.22936
ISSN
0364-9024
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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