Closure and Spanning k-Trees

Ryota Matsubara; Masao Tsugaki; Tomoki Yamashita

doi:10.1007/s00373-013-1314-z

Closure and Spanning k-Trees

Ryota Matsubara, Masao Tsugaki, Tomoki Yamashita

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (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
Pages (from-to)	957-962
Number of pages	6
Journal	Graphs and Combinatorics
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/s00373-013-1314-z
Publication status	Published - 2014 Jun

Keywords

Closure
Spanning tree
k-tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-013-1314-z

Cite this

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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.",

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AU - Matsubara, Ryota

AU - Tsugaki, Masao

AU - Yamashita, Tomoki

PY - 2014/6

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N2 - 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.

AB - 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.

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KW - Spanning tree

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Closure and Spanning k-Trees

Abstract

Keywords

ASJC Scopus subject areas

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