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Journal of Mathematical Sciences

, Volume 179, Issue 5, pp 616–620 | Cite as

Spanning trees with many leaves

  • D. V. Karpov
Article
  • 21 Downloads

Let a maximal chain of vertices of degree 2 in a graph G consist of k > 0 vertices. We prove that G has a spanning tree with more than \( \frac{{v(G)}}{{2k + 4}} \) leaves (where υ(G) is the number of vertices of the graph G). We present an infinite series of examples showing that the constant \( \frac{1}{{2k + 4}} \) cannot be enlarged. Bibliography: 7 titles.

Keywords

Russia Span Tree Mathematical Institute Infinite Series Maximal Chain 
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References

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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