### Abstract

We investigate the largest number of colours, called upper chromatic number and denoted χ̄(ℋ), that can be assigned to the vertices (points) of a Steiner triple system ℋ in such a way that every block H ∈ ℋ contains at least two vertices of the same colour. The exact value of χ̄ is determined for some classes of triple systems, and it is observed further that optimal colourings with the same number of colours exist also under the additional assumption that no monochromatic block occurs. Examples show, however, that the cardinalities of the colour classes in the latter case are more strictly determined.

Original language | English |
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Pages (from-to) | 233-243 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 182 |

Issue number | 1-3 |

Publication status | Published - Mar 1 1998 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*182*(1-3), 233-243.

**Strict colourings for classes of steiner triple systems.** / Milazzo, L.; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 182, no. 1-3, pp. 233-243.

}

TY - JOUR

T1 - Strict colourings for classes of steiner triple systems

AU - Milazzo, L.

AU - Tuza, Z.

PY - 1998/3/1

Y1 - 1998/3/1

N2 - We investigate the largest number of colours, called upper chromatic number and denoted χ̄(ℋ), that can be assigned to the vertices (points) of a Steiner triple system ℋ in such a way that every block H ∈ ℋ contains at least two vertices of the same colour. The exact value of χ̄ is determined for some classes of triple systems, and it is observed further that optimal colourings with the same number of colours exist also under the additional assumption that no monochromatic block occurs. Examples show, however, that the cardinalities of the colour classes in the latter case are more strictly determined.

AB - We investigate the largest number of colours, called upper chromatic number and denoted χ̄(ℋ), that can be assigned to the vertices (points) of a Steiner triple system ℋ in such a way that every block H ∈ ℋ contains at least two vertices of the same colour. The exact value of χ̄ is determined for some classes of triple systems, and it is observed further that optimal colourings with the same number of colours exist also under the additional assumption that no monochromatic block occurs. Examples show, however, that the cardinalities of the colour classes in the latter case are more strictly determined.

UR - http://www.scopus.com/inward/record.url?scp=0001116526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001116526&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001116526

VL - 182

SP - 233

EP - 243

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -