A k-tree containing specified vertices

Shuya Chiba, Ryota Matsubara, Kenta Ozeki, Masao Tsugaki

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)187-205
Number of pages19
JournalGraphs and Combinatorics
Volume26
Issue number2
DOIs
Publication statusPublished - 2010 Mar
Externally publishedYes

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 journalArticle

Chiba, Shuya ; Matsubara, Ryota ; Ozeki, Kenta ; Tsugaki, Masao. / A k-tree containing specified vertices. In: Graphs and Combinatorics. 2010 ; Vol. 26, No. 2. pp. 187-205.
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