### Abstract

For an undirected graph G and a natural number n, a G-design of order n is an edge partition of the complete graph K_{n} with n vertices into subgraphs G_{1},G_{2},⋯, each isomorphic to G. A set T C V(K_{n}) is called a blocking set if it meets the vertex set V(G _{i}) of each G_{i} in the decomposition, but contains none of them. In a previous paper [J. Combin. Designs 4(1996),135-142] the first and third authors proved that if G is a cycle, then there exists a G-design without blocking sets. Here we extend this theorem for all graphs G, moreover we prove that for every G and every integer k ≥ 2 there exists a non-k-colorable G-design.

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

Pages (from-to) | 229-233 |

Number of pages | 5 |

Journal | Ars Combinatoria |

Volume | 114 |

Publication status | Published - 2014 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Ars Combinatoria*,

*114*, 229-233.

**G-designs without blocking sets.** / Milici, Salvatore; Quattrocchi, Gaetano; Tuza, Z.

Research output: Contribution to journal › Article

*Ars Combinatoria*, vol. 114, pp. 229-233.

}

TY - JOUR

T1 - G-designs without blocking sets

AU - Milici, Salvatore

AU - Quattrocchi, Gaetano

AU - Tuza, Z.

PY - 2014

Y1 - 2014

N2 - For an undirected graph G and a natural number n, a G-design of order n is an edge partition of the complete graph Kn with n vertices into subgraphs G1,G2,⋯, each isomorphic to G. A set T C V(Kn) is called a blocking set if it meets the vertex set V(G i) of each Gi in the decomposition, but contains none of them. In a previous paper [J. Combin. Designs 4(1996),135-142] the first and third authors proved that if G is a cycle, then there exists a G-design without blocking sets. Here we extend this theorem for all graphs G, moreover we prove that for every G and every integer k ≥ 2 there exists a non-k-colorable G-design.

AB - For an undirected graph G and a natural number n, a G-design of order n is an edge partition of the complete graph Kn with n vertices into subgraphs G1,G2,⋯, each isomorphic to G. A set T C V(Kn) is called a blocking set if it meets the vertex set V(G i) of each Gi in the decomposition, but contains none of them. In a previous paper [J. Combin. Designs 4(1996),135-142] the first and third authors proved that if G is a cycle, then there exists a G-design without blocking sets. Here we extend this theorem for all graphs G, moreover we prove that for every G and every integer k ≥ 2 there exists a non-k-colorable G-design.

UR - http://www.scopus.com/inward/record.url?scp=84902109467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902109467&partnerID=8YFLogxK

M3 - Article

VL - 114

SP - 229

EP - 233

JO - Ars Combinatoria

JF - Ars Combinatoria

SN - 0381-7032

ER -