## Abstract Let Ξ·β>β0 be given. Then there exists __d__~0~β=β__d__~0~(Ξ·) such that the following holds. Let __G__ be a finite graph with maximum degree at most __d__ββ₯β__d__~0~ whose vertex set is partitioned into classes of size Ξ± __d__, where Ξ±β₯ 11/4β+βΞ·. Then there exists a proper coloring of __
An improved lower bound for the radio -chromatic number of the hypercube
β Scribed by Srinivasa Rao Kola; Pratima Panigrahi
- Book ID
- 108078586
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 355 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We draw the __n__βdimensional hypercube in the plane with ${5\over 32}4^{n}-\lfloor{{{{n}^{2}+1}\over 2}}\rfloor {2}^{n-2}$ crossings, which improves the previous best estimation and coincides with the long conjectured upper bound of ErdΓΆs and Guy. Β© 2008 Wiley Periodicals, Inc. J Graph
## Abstract After giving a new proof of a wellβknown theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and SzekeresβWilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edgeβcut (__V__~1~, __V_