Table of Contents
ISRN Combinatorics
Volume 2013, Article ID 672731, 13 pages
http://dx.doi.org/10.1155/2013/672731
Research Article

Holey Perfect Mendelsohn Designs of Type with Block Size Four

Computer Science Department, The University of Iowa, Iowa City, IA 52242, USA

Received 11 October 2012; Accepted 30 October 2012

Academic Editors: M. Gionfriddo and D. S. Kim

Copyright © 2013 Hantao Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 4-HPMD denote a holey perfect Mendelsohn design with block size four. The existence of 4-HPMDs with holes of size 2 and one hole of size 3, that is, of type , was established by Bennett et al. in 1997. In this paper, we investigate the existence of 4-HPMDs of type for : a 4-HPMD() exists if and only if , except possibly for , (7, 6), (11, 9), (11, 10). We also investigate the existence of 4-HPMD() for general and prove that there exists a 4-HPMD() for all . Moreover, if , then a 4-HPMD() exists for all ; if , then a 4-HPMD() exists for all .