### Abstract

The upper chromatic number χ̄(ℋ) of a set system ℋ is the maximum number of colours that can be assigned to the elements of the underlying set of ℋ in such a way that each H ∈ ℋ contains a monochromatic pair of elements. We prove that a Steiner triple system of order ν≤2^{k} - 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.

Original language | English |
---|---|

Pages (from-to) | 247-259 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 174 |

Issue number | 1-3 |

Publication status | Published - Sep 15 1997 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*174*(1-3), 247-259.

**Upper chromatic number of Steiner triple and quadruple systems.** / Milazzo, Lorenzo; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 174, no. 1-3, pp. 247-259.

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TY - JOUR

T1 - Upper chromatic number of Steiner triple and quadruple systems

AU - Milazzo, Lorenzo

AU - Tuza, Z.

PY - 1997/9/15

Y1 - 1997/9/15

N2 - The upper chromatic number χ̄(ℋ) of a set system ℋ is the maximum number of colours that can be assigned to the elements of the underlying set of ℋ in such a way that each H ∈ ℋ contains a monochromatic pair of elements. We prove that a Steiner triple system of order ν≤2k - 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.

AB - The upper chromatic number χ̄(ℋ) of a set system ℋ is the maximum number of colours that can be assigned to the elements of the underlying set of ℋ in such a way that each H ∈ ℋ contains a monochromatic pair of elements. We prove that a Steiner triple system of order ν≤2k - 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.

UR - http://www.scopus.com/inward/record.url?scp=0000795368&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000795368&partnerID=8YFLogxK

M3 - Article

VL - 174

SP - 247

EP - 259

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -