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

Haruhide Matsuda, Kenta Ozeki, Tomoki Yamashita

13 引用 (Scopus)

### 抄録

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.

元の言語 English 429-437 9 Graphs and Combinatorics 30 2 https://doi.org/10.1007/s00373-012-1277-5 Published - 2014 3

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### これを引用

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

：: Graphs and Combinatorics, 巻 30, 番号 2, 03.2014, p. 429-437.

Matsuda, Haruhide ; Ozeki, Kenta ; Yamashita, Tomoki. / Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph. ：: Graphs and Combinatorics. 2014 ; 巻 30, 番号 2. pp. 429-437.
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