#### Abstract

A single-change circular covering design (scccd) based on the set [*v*] = {1, . . . ,*v*} with block size *k* is an ordered collection of *b* blocks, * B* = {

*B*

_{1}, . . . ,

*B*

_{b}}, each

*B*⊂ [

_{i}*v*], which obey: (1) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [

*v*] is covered by some

*Bi*. The object is to minimize

*b*for a fixed

*v*and

*k*. We present some minimal constructions of scccds for arbitrary

*v*when

*k*= 2 and 3, and for arbitrary

*k*when

*k*+1 ≤ v ≤ 2

*k*. Tight designs are those in which each pair is covered exactly once. Start-Finish arrays are used to construct tight designs when

*v*> 2

*k*; there are 2 non-isomorphic tight designs with (

*v*,

*k*) = (9, 4), and 12 with (

*v*,

*k*) = (10, 4). Some non-existence results for tight designs, and standardized, element-regular, perfect, and column-regular designs are also considered.

#### Recommended Citation

McSorley, John P. "Single-Change Circular Covering Designs." (Feb 1999).

## Comments

Published in McSorley, J.P. (2008). Single-change circular covering designs.

Discrete Mathematics, 197/198, 561-588