G-designs without blocking sets

Salvatore Milici, Gaetano Quattrocchi, Z. Tuza

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Pages (from-to)229-233
Number of pages5
JournalArs Combinatoria
Volume114
Publication statusPublished - 2014

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G-design
Blocking Set
Natural number
Undirected Graph
Complete Graph
Subgraph
Isomorphic
Partition
Cycle
Decompose
Integer
Graph in graph theory
Vertex of a graph
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Milici, S., Quattrocchi, G., & Tuza, Z. (2014). G-designs without blocking sets. Ars Combinatoria, 114, 229-233.

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

In: Ars Combinatoria, Vol. 114, 2014, p. 229-233.

Research output: Contribution to journalArticle

Milici, S, Quattrocchi, G & Tuza, Z 2014, 'G-designs without blocking sets', Ars Combinatoria, vol. 114, pp. 229-233.
Milici S, Quattrocchi G, Tuza Z. G-designs without blocking sets. Ars Combinatoria. 2014;114:229-233.
Milici, Salvatore ; Quattrocchi, Gaetano ; Tuza, Z. / G-designs without blocking sets. In: Ars Combinatoria. 2014 ; Vol. 114. pp. 229-233.
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