This article is motivated by a conjecture of Thomassen and Toft on the number s 2 (G) of separating vertex sets of cardinality 2 and the number v 2 (G) of vertices of degree 2 in a graph G belonging to the class G of all 2-connected graphs without nonseparating induced cycles. Let G denote the numbe
On a construction of Thomassen
✍ Scribed by Peter Horák; Jozef Širáň
- Book ID
- 105309280
- Publisher
- Springer Japan
- Year
- 1986
- Tongue
- English
- Weight
- 263 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0911-0119
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In 1983 C. Thomassen conjectured that for every k, g ∈ N there exists d such that any graph with average degree at least d contains a subgraph with average degree at least k and girth at least g. Kühn and Osthus [2004] proved the case g = 6. We give another proof for the case g = 6 which is based