Degree conditions and degree bounded trees

Haruhide Matsuda, Hajime Matsumura

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4 Citations (Scopus)

Abstract

We give sufficient conditions for a graph to have degree bounded trees. Let G be a connected graph and A a vertex subset of G. We denote by σk (A) the minimum value of the degree sum in G of any k independent vertices in A and by w (G - A) the number of components in the induced subgraph G - A. Our main results are the following: (i) If σk (A) ≥ | V (G) | - 1, then G contains a tree T with maximum degree at most k and A ⊆ V (T). (ii) If σk - w (G - A) (A) ≥ | A | - 1, then G contains a spanning tree T such that dT (x) ≤ k for every x ∈ A. These are generalizations of the result by Win [S. Win, Existenz von Gerüsten mit Vorgeschriebenem Maximalgrad in Graphen, Abh. Math. Sem. Univ. Hamburg 43 (1975) 263-267] and the degree conditions are sharp.

Original languageEnglish
Pages (from-to)3653-3658
Number of pages6
JournalDiscrete Mathematics
Volume309
Issue number11
DOIs
Publication statusPublished - 2009 Jun 6

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Keywords

  • Degree bounded tree
  • Degree sum condition
  • Spanning tree
  • Tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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