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 |
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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
- Specified vertices
- k-Tree
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics