Two conjectures of Grünbaum on arrangements of curves
✍ Scribed by Pierre Masai
- Book ID
- 107748418
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 794 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We establish a duality principle for arrangements of pseudolines in the projective plane, and thereby prove the conjecture of Burr, Griinbaum, and Sloane that the solution T(p) of the "orchard problem" for pseudoline arrangements and the solution r(p) of the dual problem xe equa1.
## Abstract In 1976, Borodin conjectured that every planar graph has a 5‐coloring such that the union of every __k__ color classes with 1 ≤ __k__ ≤ 4 induces a (__k__—1)‐degenerate graph. We prove the existence of such a coloring using 18 colors. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:139