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- W1939767867 abstract "A group divisible design (GDD) is a triple which satisfies the following properties: (1) is a partition of X into subsets called groups; (2) is a collection of subsets of X, called blocks, such that a group and a block contain at most one element in common; and (3) every pair of elements from distinct groups occurs in a constant number λ blocks. This parameter λ is usually called the index. A k-GDD of type is a GDD with block size k, index , and u groups of size g. A GDD is resolvable if the blocks can be partitioned into classes such that each point occurs in precisely one block of each class. We denote such a design as an RGDD. For fixed integers and , we show that the necessary conditions for the existence of a k-RGDD of type are sufficient for all . As a corollary of this result and the existence of large resolvable graph decompositions, we establish the asymptotic existence of resolvable graph GDDs, G-RGDDs, whenever the necessary conditions for the existence of -RGDs are met. We also show that, with a few easy modifications, the techniques extend to general index. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 112–126, 2013" @default.
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- W1939767867 date "2012-05-01" @default.
- W1939767867 modified "2023-09-26" @default.
- W1939767867 title "The Asymptotic Existence of Resolvable Group Divisible Designs" @default.
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- W1939767867 doi "https://doi.org/10.1002/jcd.21315" @default.
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