### Abstract

In an m-cycle system script C sign of order n (n ≥ m ≥ 3 integers), the blocks are the vertex sets of n(n - 1)/(2m) cycles C_{i} of length m such that each edge of the complete graph K_{n} belongs to precisely one cycle C_{i} ∈ script C sign. We investigate m-cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of script C sign. Relatively small systems (with n ≤ 2^{m}/(em)) are always '2-colorable' in this sense; moreover, for every constant c, if n ≤ cm, then a partition into c^{1}m/log m classes exists (where the constant c^{1} depends only on c).

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

Pages (from-to) | 451-462 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 208-209 |

Publication status | Published - Oct 28 1999 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*208-209*, 451-462.

**Disjoint blocking sets in cycle systems.** / Milici, Salvatore; Tuza, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 208-209, pp. 451-462.

}

TY - JOUR

T1 - Disjoint blocking sets in cycle systems

AU - Milici, Salvatore

AU - Tuza, Z.

PY - 1999/10/28

Y1 - 1999/10/28

N2 - In an m-cycle system script C sign of order n (n ≥ m ≥ 3 integers), the blocks are the vertex sets of n(n - 1)/(2m) cycles Ci of length m such that each edge of the complete graph Kn belongs to precisely one cycle Ci ∈ script C sign. We investigate m-cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of script C sign. Relatively small systems (with n ≤ 2m/(em)) are always '2-colorable' in this sense; moreover, for every constant c, if n ≤ cm, then a partition into c1m/log m classes exists (where the constant c1 depends only on c).

AB - In an m-cycle system script C sign of order n (n ≥ m ≥ 3 integers), the blocks are the vertex sets of n(n - 1)/(2m) cycles Ci of length m such that each edge of the complete graph Kn belongs to precisely one cycle Ci ∈ script C sign. We investigate m-cycle systems which admit vertex partitions into two or more classes in such a way that each class meets every cycle of script C sign. Relatively small systems (with n ≤ 2m/(em)) are always '2-colorable' in this sense; moreover, for every constant c, if n ≤ cm, then a partition into c1m/log m classes exists (where the constant c1 depends only on c).

UR - http://www.scopus.com/inward/record.url?scp=0042782276&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042782276&partnerID=8YFLogxK

M3 - Article

VL - 208-209

SP - 451

EP - 462

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

ER -