Degree Bounded Spanning Trees

Jun Fujisawa; Hajime Matsumura; Tomoki Yamashita

doi:10.1007/s00373-010-0941-x

Degree Bounded Spanning Trees

Jun Fujisawa, Hajime Matsumura, Tomoki Yamashita

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

7 Citations (Scopus)

Abstract

In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set ⊆ of cardinality n(k-1) + c + 2, there exists a vertex set ⊆ of cardinality k such that the degree sum of vertices in X is at least {pipe}V(G){pipe} - c -1. Then G has a spanning tree T with maximum degree at most k + [c/n] and ∑_ν∈V(T) max{d_T (ν) - k, 0} ≤ c.

Original language	English
Pages (from-to)	695-720
Number of pages	26
Journal	Graphs and Combinatorics
Volume	26
Issue number	5
DOIs	https://doi.org/10.1007/s00373-010-0941-x
Publication status	Published - 2010 Sept
Externally published	Yes

Keywords

Degree bounded tree
Degree sum condition
Independence number
Spanning tree
Total excess

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-010-0941-x

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AU - Matsumura, Hajime

AU - Yamashita, Tomoki

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AB - In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set ⊆ of cardinality n(k-1) + c + 2, there exists a vertex set ⊆ of cardinality k such that the degree sum of vertices in X is at least {pipe}V(G){pipe} - c -1. Then G has a spanning tree T with maximum degree at most k + [c/n] and ∑ν∈V(T) max{dT (ν) - k, 0} ≤ c.

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KW - Degree sum condition

KW - Independence number

KW - Spanning tree

KW - Total excess

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Degree Bounded Spanning Trees

Abstract

Keywords

ASJC Scopus subject areas

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