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 language | English |
|---|---|
| Pages (from-to) | 429-437 |
| Number of pages | 9 |
| Journal | Graphs and Combinatorics |
| Volume | 30 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 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 journal › Article
}
TY - JOUR
T1 - Spanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph
AU - Matsuda, Haruhide
AU - Ozeki, Kenta
AU - Yamashita, Tomoki
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
KW - Branch vertices
KW - Claw-free graphs
KW - Spanning trees
UR - http://www.scopus.com/inward/record.url?scp=84894300730&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84894300730&partnerID=8YFLogxK
U2 - 10.1007/s00373-012-1277-5
DO - 10.1007/s00373-012-1277-5
M3 - Article
VL - 30
SP - 429
EP - 437
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
SN - 0911-0119
IS - 2
ER -