# Closure and Spanning k-Trees

Ryota Matsubara, Masao Tsugaki, Tomoki Yamashita

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

In this paper, we propose a new closure concept for spanning k-trees. A k-tree is a tree with maximum degree at most k. We prove that: Let G be a connected graph and let u and v be nonadjacent vertices of G. Suppose that (Formula presented) for every independent set S in G of order k with u, v ∈ S. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. This result implies Win's result (Abh Math Sem Univ Hamburg, 43:263-267, 1975) and Kano and Kishimoto's result (Graph Comb, 2013) as corollaries.

Original language English 957-962 6 Graphs and Combinatorics 30 4 https://doi.org/10.1007/s00373-013-1314-z Published - 2014

### Keywords

• Closure
• k-tree
• Spanning tree

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

Closure and Spanning k-Trees. / Matsubara, Ryota; Tsugaki, Masao; Yamashita, Tomoki.

In: Graphs and Combinatorics, Vol. 30, No. 4, 2014, p. 957-962.

Research output: Contribution to journalArticle

Matsubara, Ryota ; Tsugaki, Masao ; Yamashita, Tomoki. / Closure and Spanning k-Trees. In: Graphs and Combinatorics. 2014 ; Vol. 30, No. 4. pp. 957-962.
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