A k-tree containing specified vertices

Shuya Chiba, Ryota Matsubara, Kenta Ozeki, Masao Tsugaki

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)187-205
Number of pages19
JournalGraphs and Combinatorics
Issue number2
Publication statusPublished - 2010 Mar
Externally publishedYes


  • Degree sum
  • Specified vertices
  • k-Tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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