Spanning trees with a bounded number of leaves in a claw-free graph

Mikio Kano; Aung Kyaw; Haruhide Matsuda; Kenta Ozeki; Akira Saito; Tomoki Yamashita

Spanning trees with a bounded number of leaves in a claw-free graph

Mikio Kano, Aung Kyaw, Haruhide Matsuda, Kenta Ozeki, Akira Saito, Tomoki Yamashita

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

Abstract

For a graph H and an integer K ≥ 2, let σ _k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ _k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

Original language	English
Pages (from-to)	137-154
Number of pages	18
Journal	Ars Combinatoria
Volume	103
Publication status	Published - 2012 Jan 1

Keywords

Claw-free graphs
Degree sum
Leaf
Spanning tree

ASJC Scopus subject areas

Mathematics(all)

Cite this

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abstract = "For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.",

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T1 - Spanning trees with a bounded number of leaves in a claw-free graph

AU - Kano, Mikio

AU - Kyaw, Aung

AU - Matsuda, Haruhide

AU - Ozeki, Kenta

AU - Saito, Akira

AU - Yamashita, Tomoki

PY - 2012/1/1

Y1 - 2012/1/1

N2 - For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

AB - For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

KW - Claw-free graphs

KW - Degree sum

KW - Leaf

KW - Spanning tree

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ER -

Spanning trees with a bounded number of leaves in a claw-free graph

Abstract

Keywords

ASJC Scopus subject areas

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