### Abstract

An equivalence graph is a vertex disjoint union of complete graphs. For a graph G, let eq(G) be the minimum number of equivalence subgraphs of G needed to cover all edges of G. Similarly, let cc(G) be the minimum number of complete subgraphs of G needed to cover all its edges. Let H be a graph on n vertices with maximal degree ≦d (and minimal degree ≧1), and let G= {Mathematical expression} be its complement. We show that {Mathematical expression} The lower bound is proved by multilinear techniques (exterior algebra), and its assertion for the complement of an n-cycle settles a problem of Frankl. The upper bound is proved by probabilistic arguments, and it generalizes results of de Caen, Gregory and Pullman.

Original language | English (US) |
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Pages (from-to) | 201-206 |

Number of pages | 6 |

Journal | Combinatorica |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Mathematics

### Keywords

- AMS subject classification (1980): 68E10, 68E05, 05B25, 05C55