## Abstract

A graph (Formula presented.) is said to be (Formula presented.) -ubiquitous, where (Formula presented.) is the minor relation between graphs, if whenever (Formula presented.) is a graph with (Formula presented.) for all (Formula presented.), then one also has (Formula presented.), where (Formula presented.) is the disjoint union of (Formula presented.) many copies of (Formula presented.). A well-known conjecture of Andreae is that every locally finite connected graph is (Formula presented.) -ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph (Formula presented.) which implies that (Formula presented.) is (Formula presented.) -ubiquitous. In particular this implies that the full-grid is (Formula presented.) -ubiquitous.

Original language | English |
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Number of pages | 38 |

Journal | Journal of Graph Theory |

Early online date | 2023 |

DOIs | |

Publication status | E-pub ahead of print - 2023 |

## Keywords

- graph minors
- infinite graphs
- ubiquity

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Geometry and Topology