Degree Conditions for Graphs to Have Spanning Trees with Few Branch Vertices and Leaves

Shun ichi Maezawa, Ryota Matsubara, Haruhide Matsuda

Research output: Contribution to journalArticle


A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree strictly greater than two. This paper shows two degree conditions for graphs to have spanning trees with total bounded number of branch vertices and leaves. Moreover, the sharpness of our results is shown.

Original languageEnglish
Pages (from-to)231-238
Number of pages8
JournalGraphs and Combinatorics
Issue number1
Publication statusPublished - 2019 Jan 2



  • Branch vertex
  • Fan-type degree condition
  • Leaf
  • Spanning tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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