Closure and Spanning k-Trees

Ryota Matsubara, Masao Tsugaki, Tomoki Yamashita

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)957-962
Number of pages6
JournalGraphs and Combinatorics
Issue number4
Publication statusPublished - 2014 Jun


  • Closure
  • Spanning tree
  • k-tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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