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Maximum Spanning Trees in Normed Planes

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Abstract

Extending some properties from the Euclidean plane to any normed plane, we show the validity of the Monma–Paterson–Suri–Yao algorithm for finding the maximum-weighted spanning tree of a set of n points, where the weight of an edge is the distance between the end points measured by the norm and there are not repeated distances. For strictly convex normed planes, we expose a strategy for moving slightly the points of the set in order to obtain distinct distances.

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Acknowledgements

The authors gratefully thank Professor Pier Luigi Papini for his useful comments and suggestions. We greatly appreciate the reviewers indications that really improve the paper.

Funding

Pedro Martín is partially supported by Junta de Extremadura/FEDER Grants numbers IB18023 and GR18023.

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Authors and Affiliations

  1. Instituto de Matemáticas (IMUEx), UEx, 06006, Badajoz, Spain

    Javier Alonso

  2. Departamento de Matemáticas, Instituto de Matemáticas (IMUEx), UEx, 06006, Badajoz, Spain

    Pedro Martín

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  1. Javier Alonso
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  2. Pedro Martín
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Correspondence to Pedro Martín.

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Alonso, J., Martín, P. Maximum Spanning Trees in Normed Planes. Graphs and Combinatorics 37, 1385–1403 (2021). https://doi.org/10.1007/s00373-021-02325-6

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  • DOI: https://doi.org/10.1007/s00373-021-02325-6

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