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A Full Halin Grid Theorem.

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Title: A Full Halin Grid Theorem.
Authors: Georgakopoulos, Agelos1 (AUTHOR) Georgakopoulos@warwick.ac.uk, Hamann, Matthias2 (AUTHOR)
Source: Discrete & Computational Geometry. Jun2026, Vol. 75 Issue 4, p1060-1072. 13p.
Subjects: Graph theory, Regular graphs
Abstract: Halin's well-known grid theorem states that a graph G with a thick end must contain a subdivision of the hexagonal half-grid. We obtain the following strengthening when G is vertex-transitive and locally finite. Either G is quasi-isometric to a tree (and therefore has no thick end), or it contains a subdivision of the full hexagonal grid. [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Halin's well-known grid theorem states that a graph G with a thick end must contain a subdivision of the hexagonal half-grid. We obtain the following strengthening when G is vertex-transitive and locally finite. Either G is quasi-isometric to a tree (and therefore has no thick end), or it contains a subdivision of the full hexagonal grid. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00454-024-00707-0
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        Text: English
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              Text: Jun2026
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