TY - JOUR
T1 - Kirkman school project designs
AU - Colbourn, Charles J.
AU - Ling, Alan C.H.
N1 - Funding Information:
Thanks are due to the two referees for helpful comments. The research of the first author is supported by ARO grant DAAG55-98-1-0272.
PY - 1999/5/28
Y1 - 1999/5/28
N2 - A Kirkman school project design on v elements consists of the maximum admissible number of disjoint parallel classes, each containing blocks of sizes three except possibly one of size two or four. Černý, Horák, and Wallis completely settled existence when v ≡ 0,2 (mod 3) and made some progress and advanced a conjecture when v ≡ 1 (mod 3). In this paper, a complete solution for the existence of such designs when v ≡ 4 (mod 6) is given, and a nearly complete solution when v ≡ 1 (mod6) is also given.
AB - A Kirkman school project design on v elements consists of the maximum admissible number of disjoint parallel classes, each containing blocks of sizes three except possibly one of size two or four. Černý, Horák, and Wallis completely settled existence when v ≡ 0,2 (mod 3) and made some progress and advanced a conjecture when v ≡ 1 (mod 3). In this paper, a complete solution for the existence of such designs when v ≡ 4 (mod 6) is given, and a nearly complete solution when v ≡ 1 (mod6) is also given.
UR - http://www.scopus.com/inward/record.url?scp=0041167318&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0041167318&partnerID=8YFLogxK
U2 - 10.1016/S0012-365X(99)00015-1
DO - 10.1016/S0012-365X(99)00015-1
M3 - Article
AN - SCOPUS:0041167318
SN - 0012-365X
VL - 203
SP - 49
EP - 60
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -