On a spanning tree with specified leaves

Yoshimi Egawa, Haruhide Matsuda, Tomoki Yamashita, Kiyoshi Yoshimoto

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)13-18
Number of pages6
JournalGraphs and Combinatorics
Volume24
Issue number1
DOIs
Publication statusPublished - 2008 Feb 1

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Keywords

  • Hamilton path
  • Hamilton-connected
  • Leaf-connected
  • Spanning tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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