On partitioning minimum spanning trees

Nili Guttmann-Beck; Refael Hassin; Michal Stern

doi:10.1016/j.dam.2024.07.025

On partitioning minimum spanning trees

Nili Guttmann-Beck, Refael Hassin, Michal Stern

Research output: Contribution to journal › Article › peer-review

Abstract

Let V be a set of points in the plane, and T the edge set of a minimum spanning tree of the complete graph induced by V. We prove that partitioning every edge of T into k equal parts, under Mahalanobis-norm, yields a Minimum Spanning Tree on the new set of points. We also prove that partitioning every edge of T in any symmetric way, under the Euclidean norm in 2-dimension space, yields a Minimum Spanning Tree on the new set of points. However, these properties break down under the ℓ₁ or ℓ_∞ norms.

Original language	English
Pages (from-to)	45-54
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	359
DOIs	https://doi.org/10.1016/j.dam.2024.07.025
State	Published - 31 Dec 2024
Externally published	Yes

Keywords

Minimum spanning tree

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2024.07.025

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On partitioning minimum spanning trees

Abstract

Keywords

ASJC Scopus subject areas

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