We prove that the vertex set of a simple graph with minimum degree at least s + t -1 and girth at least 5 can be decomposed into two parts, which induce subgraphs with minimum degree at least s and t, respectively, where s, t are positive integers β₯ 2.
Decomposing graphs under degree constraints
β Scribed by Stiebitz, Michael
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 246 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
We prove a conjecture of C. Thomassen: If s and t are non-negative integers, and if G is a graph with minimum degree s + t + 1, then the vertex set of G can be partitioned into two sets which induce subgraphs of minimum degree at least s and t , respectively.
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