Abstract
A k-tree is a tree with maximum degree at most k. In this paper, we give sufficient conditions for a graph to have a k-tree containing specified vertices. Let k be an integer with k ≥ 3. Let G be a graph of order n and let S ⊆ V(G) with κ(S) ≥ 1. Suppose that for every l ≥ κ(S), there exists an integer t such that l≤t≤(k-1)l+2-{down left corner}k/l-1 and the degree sum of any t independent vertices of S is at least n + tl - kl - 1. Then G has a k-tree containing S. We also show some new results on a spanning k-tree as corollaries of the above theorem.
| Original language | English |
|---|---|
| Pages (from-to) | 187-205 |
| Number of pages | 19 |
| Journal | Graphs and Combinatorics |
| Volume | 26 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2010 Mar |
| Externally published | Yes |
Keywords
- Degree sum
- k-Tree
- Specified vertices
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
Cite this
A k-tree containing specified vertices. / Chiba, Shuya; Matsubara, Ryota; Ozeki, Kenta; Tsugaki, Masao.
In: Graphs and Combinatorics, Vol. 26, No. 2, 03.2010, p. 187-205.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A k-tree containing specified vertices
AU - Chiba, Shuya
AU - Matsubara, Ryota
AU - Ozeki, Kenta
AU - Tsugaki, Masao
PY - 2010/3
Y1 - 2010/3
N2 - A k-tree is a tree with maximum degree at most k. In this paper, we give sufficient conditions for a graph to have a k-tree containing specified vertices. Let k be an integer with k ≥ 3. Let G be a graph of order n and let S ⊆ V(G) with κ(S) ≥ 1. Suppose that for every l ≥ κ(S), there exists an integer t such that l≤t≤(k-1)l+2-{down left corner}k/l-1 and the degree sum of any t independent vertices of S is at least n + tl - kl - 1. Then G has a k-tree containing S. We also show some new results on a spanning k-tree as corollaries of the above theorem.
AB - A k-tree is a tree with maximum degree at most k. In this paper, we give sufficient conditions for a graph to have a k-tree containing specified vertices. Let k be an integer with k ≥ 3. Let G be a graph of order n and let S ⊆ V(G) with κ(S) ≥ 1. Suppose that for every l ≥ κ(S), there exists an integer t such that l≤t≤(k-1)l+2-{down left corner}k/l-1 and the degree sum of any t independent vertices of S is at least n + tl - kl - 1. Then G has a k-tree containing S. We also show some new results on a spanning k-tree as corollaries of the above theorem.
KW - Degree sum
KW - k-Tree
KW - Specified vertices
UR - http://www.scopus.com/inward/record.url?scp=77953322425&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77953322425&partnerID=8YFLogxK
U2 - 10.1007/s00373-010-0903-3
DO - 10.1007/s00373-010-0903-3
M3 - Article
AN - SCOPUS:77953322425
VL - 26
SP - 187
EP - 205
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
SN - 0911-0119
IS - 2
ER -