Abstract
In their seminal paper on geometric minimum spanning trees, Monma and Suri [6] gave a method to embed any tree of maximal degree 5 as a minimum spanning tree in the Euclidean plane. They derived area bounds of \(O(2^{k^2} \times 2^{k^2})\) for trees of height k and conjectured that an improvement below c n ×c n is not possible for some constant c > 0. We partially disprove this conjecture by giving polynomial area bounds for arbitrary trees of maximal degree 3 and 4.
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Kaufmann, M. (2008). Polynomial Area Bounds for MST Embeddings of Trees. In: Hong, SH., Nishizeki, T., Quan, W. (eds) Graph Drawing. GD 2007. Lecture Notes in Computer Science, vol 4875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77537-9_12
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DOI: https://doi.org/10.1007/978-3-540-77537-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77536-2
Online ISBN: 978-3-540-77537-9
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