Ramsey-Type Theorems for Spatial Graphs and Good Drawings
✍ Scribed by Seiya Negami
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 336 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
✦ Synopsis
We shall prove that for any spatial graph H, there exists a pair of natural numbers (N, M) such that any spatial embedding of the complete bipartite graph K N, M whose projection is a good drawing on the plane contains a subgraph which is ambient isotopic to a subdivision of H.
1998 Academic Press
His proof consists of four steps, translating a topological problem into a combinatorial one. Modifying this process, Miyauchi [4] has proved a similar theorem with the complete bipartite graph K N, M instead of K N . The rectilinearity cannot be omitted in these theorems. For example, we can exclude a given spatial graph H from a spatial K N , making a local knot on Article No. TB971783 53 0095-8956Â98 25.00