## Abstract In this article, we settle a problem which originated in 4 regarding the existence of resolvable (__K__~4~βββ__e__)βdesign. We solve the problem with two possible exceptions. Β© 2007 Wiley Periodicals, Inc. J Combin Designs 15: 502β510, 2007
A survey on the existence of G-Designs
β Scribed by Peter Adams; Darryn Bryant; Melinda Buchanan
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 329 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
A Gβdesign of order n is a decomposition of the complete graph on n vertices into edgeβdisjoint subgraphs isomorphic to G. We survey the current state of knowledge on the existence problem for Gβdesigns. This includes references to all the necessary designs and constructions, as well as a few new designs. Β© 2007 Wiley Periodicals, Inc. J Combin Designs 16: 373β410, 2008
π SIMILAR VOLUMES
## Abstract A set of trivial necessary conditions for the existence of a large set of __t__βdesigns, __LS__[N](__t,k,__Ξ½), is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for __i__β=β0,β¦,__t__. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary condi
## Abstract In this note, a golf design of order 41 is constructed. Combined Colbourn and Nonay's result, the existence spectrum of golf design of order Ο is the set {Ο : Ο β‘1 (mod 2), Ο ββ₯β3, Ο ββ β5}. Β© 2005 Wiley Periodicals, Inc. J Combin Designs 15: 84β89, 2007
symmetric designs with parameters (105, 40, 15) was shown.