Spanning trees with bounded degrees


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.

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Neumann-Lara, V., Rivera-Campo, E. Spanning trees with bounded degrees. Combinatorica 11, 55–61 (1991).

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AMS subject classification (1980)

  • 05 C 05


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