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Spanning \(k\)-Forests with Large Components in \(K_{1,k+1}\)-Free Graphs

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Abstract

For an integer \(k\) with \(k \ge 2\), a \(k\)-tree (resp. a \(k\)-forest) is a tree (resp. forest) with maximum degree at most \(k\). In this paper, we show that for any integer \(k\) with \(k \ge 3\), any connected \(K_{1,k+1}\)-free graph has a spanning \(k\)-tree or a spanning \(k\)-forest with only large components.

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Acknowledgments

The authors would like to thank two anonymous referees for their valuable suggestions and corrections on an earlier version of this paper.

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Authors and Affiliations

  1. National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo , 101-8430, Japan

    Kenta Ozeki

  2. JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

    Kenta Ozeki

  3. Department of Communication and Information Science, Fukushima National College of Technology, 30 Nagao Kamiarakawa Taira Iwaki, Fukushima, 970-8034, Japan

    Takeshi Sugiyama

Authors
  1. Kenta Ozeki
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  2. Takeshi Sugiyama
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Correspondence to Takeshi Sugiyama.

Additional information

This work was supported by JSPS KAKENHI Grant number 25871053.

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Ozeki, K., Sugiyama, T. Spanning \(k\)-Forests with Large Components in \(K_{1,k+1}\)-Free Graphs. Graphs and Combinatorics 31, 1659–1677 (2015). https://doi.org/10.1007/s00373-014-1434-0

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  • DOI: https://doi.org/10.1007/s00373-014-1434-0

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