Closure for spanning trees and distant area

Jun Fujisawa, Akira Saito, Ingo Schiermeyer

Research output: Contribution to journalArticle

Abstract

A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with degG u + degG v ≥ n - 1, G has a spanning k-ended tree if and only if G + uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. We investigate the relationship between the condition on degG u + degG v and the structure of the distant area for u and v. We prove that if the distant area contains Kr, we can relax the lower bound of degG u+degG v from n - 1 to n - r. And if the distant area itself is a complete graph and G is 2-connected, we can entirely remove the degree sum condition.

Original languageEnglish
Pages (from-to)143-159
Number of pages17
JournalDiscussiones Mathematicae - Graph Theory
Volume31
Issue number1
Publication statusPublished - 2011
Externally publishedYes

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K-tree
Spanning tree
Closure
Degree Sum
Induced Subgraph
Complete Graph
Adjacent
Lower bound
If and only if
Graph in graph theory

Keywords

  • closure
  • k-ended tree
  • spanning tree

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Closure for spanning trees and distant area. / Fujisawa, Jun; Saito, Akira; Schiermeyer, Ingo.

In: Discussiones Mathematicae - Graph Theory, Vol. 31, No. 1, 2011, p. 143-159.

Research output: Contribution to journalArticle

Fujisawa, J, Saito, A & Schiermeyer, I 2011, 'Closure for spanning trees and distant area', Discussiones Mathematicae - Graph Theory, vol. 31, no. 1, pp. 143-159.
Fujisawa, Jun ; Saito, Akira ; Schiermeyer, Ingo. / Closure for spanning trees and distant area. In: Discussiones Mathematicae - Graph Theory. 2011 ; Vol. 31, No. 1. pp. 143-159.
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