On a spanning tree with specified leaves

Yoshimi Egawa; Haruhide Matsuda; Tomoki Yamashita; Kiyoshi Yoshimoto

doi:10.1007/s00373-007-0768-2

On a spanning tree with specified leaves

Yoshimi Egawa, Haruhide Matsuda, Tomoki Yamashita, Kiyoshi Yoshimoto

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

8 Citations (Scopus)

Abstract

Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V(G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore's theorem which guarantees the existence of a Hamilton path connecting any two vertices.

Original language	English
Pages (from-to)	13-18
Number of pages	6
Journal	Graphs and Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00373-007-0768-2
Publication status	Published - 2008 Feb
Externally published	Yes

Keywords

Hamilton path
Hamilton-connected
Leaf-connected
Spanning tree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-007-0768-2

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AU - Yamashita, Tomoki

AU - Yoshimoto, Kiyoshi

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AB - Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V(G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore's theorem which guarantees the existence of a Hamilton path connecting any two vertices.

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KW - Spanning tree

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On a spanning tree with specified leaves

Abstract

Keywords

ASJC Scopus subject areas

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