# Degree conditions and degree bounded trees

Haruhide Matsuda, Hajime Matsumura

4 引用 (Scopus)

### 抄録

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.

元の言語 English 3653-3658 6 Discrete Mathematics 309 11 https://doi.org/10.1016/j.disc.2007.12.099 Published - 2009 6 6 Yes

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### これを引用

Degree conditions and degree bounded trees. / Matsuda, Haruhide; Matsumura, Hajime.

：: Discrete Mathematics, 巻 309, 番号 11, 06.06.2009, p. 3653-3658.

Matsuda, Haruhide ; Matsumura, Hajime. / Degree conditions and degree bounded trees. ：: Discrete Mathematics. 2009 ; 巻 309, 番号 11. pp. 3653-3658.
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