### Abstract

Suppose G_{ n}={G_{ 1}, ..., G_{ k} } is a collection of graphs, all having n vertices and e edges. By a U-decomposition of G_{ n} we mean a set of partitions of the edge sets E(G_{ t} ) of the G_{ i}, say E(G_{ t} )== {Mathematical expression} E_{ ij}, such that for each j, all the E_{ ij}, 1≦i≦k, are isomorphic as graphs. Define the function U(G_{ n}) to be the least possible value of r a U-decomposition of G_{ n} can have. Finally, let U_{ k} (n) denote the largest possible value U(G) can assume where G ranges over all sets of k graphs having n vertices and the same (unspecified) number of edges. In an earlier paper, the authors showed that {Mathematical expression} In this paper, the value of U_{ k} (n) is investigated for k>2. It turns out rather unexpectedly that the leading term of U_{ k} (n) does not depend on k. In particular we show {Mathematical expression}

Original language | English |
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Pages (from-to) | 13-24 |

Number of pages | 12 |

Journal | Combinatorica |

Volume | 1 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 1981 |

### Keywords

- AMS subject classification (1980): 05C35

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

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## Cite this

*Combinatorica*,

*1*(1), 13-24. https://doi.org/10.1007/BF02579173