### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 49-60 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 203 |

Issue number | 1-3 |

State | Published - May 28 1999 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*203*(1-3), 49-60.

**Kirkman school project designs.** / Colbourn, Charles; Ling, Alan C H.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 203, no. 1-3, pp. 49-60.

}

TY - JOUR

T1 - Kirkman school project designs

AU - Colbourn, Charles

AU - Ling, Alan C H

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

M3 - Article

AN - SCOPUS:0041167318

VL - 203

SP - 49

EP - 60

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -