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

11 Citations (Scopus)

Abstract

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
Volume30
Issue number2
DOIs
Publication statusPublished - 2014 Mar

Keywords

  • Branch vertices
  • Claw-free graphs
  • Spanning trees

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph. / Matsuda, Haruhide; Ozeki, Kenta; Yamashita, Tomoki.

In: Graphs and Combinatorics, Vol. 30, No. 2, 03.2014, p. 429-437.

Research output: Contribution to journalArticle

Matsuda, Haruhide ; Ozeki, Kenta ; Yamashita, Tomoki. / Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph. In: Graphs and Combinatorics. 2014 ; Vol. 30, No. 2. pp. 429-437.
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