## Abstract

An H-decomposition of a graph G is a partition of the edge-set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in distinct H-decompositions intersect in at most one edge. In case G = K_{n} and H = K_{r}, a k-orthogonal K_{r}-decomposition of K_{n} is called an (n, r, k) completely reducible super-simple design. We prove that for any two fixed integers r and k, there exists N = N(k, r) such that for every n > N, if K_{n} has a K_{r}-decomposition, then K_{n} also has an (n, r, k) completely-reducible super-simple design. If K_{n} does not have a K_{r}-decomposition, we show how to obtain a k-orthogonal optimal K_{r}-packing of K_{n} . Complexity issues of k-orthogonal H-decompositions are also treated.

Original language | English |
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Pages (from-to) | 93-111 |

Number of pages | 19 |

Journal | Journal of Combinatorial Theory - Series A |

Volume | 88 |

Issue number | 1 |

DOIs | |

State | Published - Oct 1999 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics