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Constructing a spanning tree with many leaves

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It was shown by Griggs and Wu that a graph of minimal degree 4 on n vertices has a spanning tree with at least \( \frac{2}{5} \) n leaves, which is asymptomatically the best possible bound for this class of graphs. In this paper, we present a polynomial time algorithm that finds in any graph with k vertices of degree greater than or equal to 4 and k′ vertices of degree 3 a spanning tree with \( \left[ {\frac{2}{5} \cdot k + \frac{2}{{15}} \cdot k'} \right] \) leaves.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    N. Gravin

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  1. N. Gravin
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Correspondence to N. Gravin.

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Translated from Zaposki Nauchnykh Seminarov POMI, Vol. 381, 2010, pp. 31–46.

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Gravin, N. Constructing a spanning tree with many leaves. J Math Sci 179, 592–600 (2011). https://doi.org/10.1007/s10958-011-0611-4

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  • DOI: https://doi.org/10.1007/s10958-011-0611-4

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