TY - JOUR

T1 - The existence of 2 × 4 grid-block designs and their applications

AU - Mutoh, Yukiyasu

AU - Morihara, Toshio

AU - Jimbo, Masakazu

AU - Fu, Hung-Lin

PY - 2003/2/1

Y1 - 2003/2/1

N2 - Fu, Hwang, Jimbo, Mutoh, and Shiue [J. Statist. Plann. Inference, to appear] introduced the concept of a grid-block design, which is defined as follows: For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block design if every two distinct points i and j in V occur exactly once in the same row or in the same column. This design has originated from the use of DNA library screening. They gave some general constructions and proved the existence of 3 × 3 grid-block designs. Meanwhile, the existence of 2 × 3 grid-block designs was shown by Carter [Designs on Cubic Multigraphs, Ph.D. thesis, McMaster University, Hamilton, ON, Canada, 1989] by decomposing Kv into cubic graphs. In this paper, we show the existence of 2 × 4 grid-block designs.

AB - Fu, Hwang, Jimbo, Mutoh, and Shiue [J. Statist. Plann. Inference, to appear] introduced the concept of a grid-block design, which is defined as follows: For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block design if every two distinct points i and j in V occur exactly once in the same row or in the same column. This design has originated from the use of DNA library screening. They gave some general constructions and proved the existence of 3 × 3 grid-block designs. Meanwhile, the existence of 2 × 3 grid-block designs was shown by Carter [Designs on Cubic Multigraphs, Ph.D. thesis, McMaster University, Hamilton, ON, Canada, 1989] by decomposing Kv into cubic graphs. In this paper, we show the existence of 2 × 4 grid-block designs.

KW - Graph decomposition

KW - Graph design

KW - Grid-block

UR - http://www.scopus.com/inward/record.url?scp=0038137172&partnerID=8YFLogxK

U2 - 10.1137/S0895480101387364

DO - 10.1137/S0895480101387364

M3 - Article

AN - SCOPUS:0038137172

VL - 16

SP - 173

EP - 178

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -