On partitioning minimum spanning trees

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 & ell;1 or & ell;infinity norms. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.