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.
本文言語 | English |
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ページ(範囲) | 429-437 |
ページ数 | 9 |
ジャーナル | Graphs and Combinatorics |
巻 | 30 |
号 | 2 |
DOI | |
出版ステータス | Published - 2014 3月 |
ASJC Scopus subject areas
- 理論的コンピュータサイエンス
- 離散数学と組合せ数学