The current smallest convex universal cover for sets of unit diameter is described. This reduction of Sprague's cover is by 4-10-J 1 and results in an asymmetrical cover. Another small universal cover of sets of unit diameter with an axis of symmetry reduces Sprague's cover by 0.0019. An indication
Covering a planar domain with sets of small diameter
โ Scribed by A. Heppes
- Publisher
- Springer Netherlands
- Year
- 2006
- Tongue
- English
- Weight
- 556 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0031-5303
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we prove the following result: THEOREM. Let K be a planar set of constant width 6; if {Bt, B2, B3} is a cover of K, in which the diameters d (Bi), where i = 1, 2, 3, are smaller than ~, then d(nl The proof is an immediate consequence of the three lemmas of Section 2. 1. NOTATION
## Abstract MacGillivray and Seyffarth (J Graph Theory 22 (1996), 213โ229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrar