Spanning trees with bounded degrees

Abstract

Lets andk be positive integers. We prove that ifG is ak-connected graph containing no independent set withks+2 vertices thenG has a spanning tree with maximum degree at mosts+1. Moreover ifs≥3 and the independence number α(G) is such that α(G)≤1+k(s−1)+c for some0≤c≤k thenG has a spanning tree with no more thanc vertices of degrees+1.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    V. Chvátal, andP. Erdős: A note on Hamiltonian Paths,Discrete Mathematics,2 (1972), 111–113.

    Google Scholar 

  2. [2]

    S. Win: On a conjecture of Las Vergnas Concerning Certain Spanning Trees in Graphs,Resultate der Mathematik,2, 215–224.

  3. [3]

    S. Win: Existenz von Gerüsten mit Vorgeschriebenem Maximalgrad in Graphen,Abhandlungen Aus dem Mathematischen Seminar der Universität Hamburg,43 (1975), 263–267.

    Google Scholar 

  4. [4]

    M. A. Gurgel, andY. Wakabayashi: Onk-leaf-connected graphs,Journal of Combinatorial Theory, Series B41 (1986), 1–16.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Neumann-Lara, V., Rivera-Campo, E. Spanning trees with bounded degrees. Combinatorica 11, 55–61 (1991). https://doi.org/10.1007/BF01375473

Download citation

AMS subject classification (1980)

  • 05 C 05

Keywords

  • Spanning tree
  • maximum degree
  • k-connected graph and independence number