Planar Graphs Have 1-string Representations
✍ Scribed by Jérémie Chalopin; Daniel Gonçalves; Pascal Ochem
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 848 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0179-5376
No coin nor oath required. For personal study only.
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We show that complements of planar graphs have intersection representations by convex sets in the plane, i.e., for every planar graph, one can assign convex sets in the plane to its vertices in such a way that two of the sets are disjoint if and only if the correspondning vertices are adjacent. This
## Abstract We provide a new method for extending results on finite planar graphs to the infinite case. Thus a result of Ungar on finite graphs has the following extension: Every infinite, planar, cubic, cyclically 4‐edge‐connected graph has a representation in the plane such that every edge is a h