Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph

Haruhide Matsuda, Kenta Ozeki, Tomoki Yamashita

Research output: Contribution to journalArticle

13 Citations (Scopus)


Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three. We show two sufficient conditions for a connected claw-free graph to have a spanning tree with a bounded number of branch vertices: (i) A connected claw-free graph has a spanning tree with at most k branch vertices if its independence number is at most 2k + 2. (ii) A connected claw-free graph of order n has a spanning tree with at most one branch vertex if the degree sum of any five independent vertices is at least n - 2. These conditions are best possible. A related conjecture also is proposed.

Original languageEnglish
Pages (from-to)429-437
Number of pages9
JournalGraphs and Combinatorics
Issue number2
Publication statusPublished - 2014 Mar 1



  • Branch vertices
  • Claw-free graphs
  • Spanning trees

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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