### Abstract

Vertex colorings of Steiner systems S(t,t + l,v) are considered in which each block contains at least two vertices of the same color. Necessary conditions for the existence of such colorings with given parameters are determined, and an upper bound of the order O(ln v) is found for the maximum number of colors. This bound remains valid for nearly complete partial Steiner systems, too. In striking contrast, systems S(t,k,v) with k ≥ t + 2 always admit colorings with at least c · v ^{a} colors, for some positive constants c and α, as v → ∞.

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

Pages (from-to) | 213-223 |

Number of pages | 11 |

Journal | Ars Combinatoria |

Volume | 92 |

Publication status | Published - Jul 2009 |

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### Keywords

- Mixed hypergraph
- Steiner system
- Upper chromatic number
- Vertex coloring

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Ars Combinatoria*,

*92*, 213-223.

**Logarithmic upper bound for the upper chromatic number of S(t, t + 1,v) systems.** / Milazzo, Lorenzo; Tuza, Z.

Research output: Contribution to journal › Article

*Ars Combinatoria*, vol. 92, pp. 213-223.

}

TY - JOUR

T1 - Logarithmic upper bound for the upper chromatic number of S(t, t + 1,v) systems

AU - Milazzo, Lorenzo

AU - Tuza, Z.

PY - 2009/7

Y1 - 2009/7

N2 - Vertex colorings of Steiner systems S(t,t + l,v) are considered in which each block contains at least two vertices of the same color. Necessary conditions for the existence of such colorings with given parameters are determined, and an upper bound of the order O(ln v) is found for the maximum number of colors. This bound remains valid for nearly complete partial Steiner systems, too. In striking contrast, systems S(t,k,v) with k ≥ t + 2 always admit colorings with at least c · v a colors, for some positive constants c and α, as v → ∞.

AB - Vertex colorings of Steiner systems S(t,t + l,v) are considered in which each block contains at least two vertices of the same color. Necessary conditions for the existence of such colorings with given parameters are determined, and an upper bound of the order O(ln v) is found for the maximum number of colors. This bound remains valid for nearly complete partial Steiner systems, too. In striking contrast, systems S(t,k,v) with k ≥ t + 2 always admit colorings with at least c · v a colors, for some positive constants c and α, as v → ∞.

KW - Mixed hypergraph

KW - Steiner system

KW - Upper chromatic number

KW - Vertex coloring

UR - http://www.scopus.com/inward/record.url?scp=67651007824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67651007824&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67651007824

VL - 92

SP - 213

EP - 223

JO - Ars Combinatoria

JF - Ars Combinatoria

SN - 0381-7032

ER -