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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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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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