### Abstract

A k-hypergraph G has vertex-set V(G) and edge-set E(G) consisting of k-subsets of V(G). If uε{lunate}V(G), then those edges of G containing u define a (k-1)-hypergraph G_{u}. We say G subsumes the (k-1)-hypergraphs {G_{u}|;uε{lunate}V(G)}. Given n graphs (i.e., 2-hyperegraphs) g_{1}, g_{2}, ... g_{n}, is there a 3-hypergraph G such that the subsumed graphs G_{i}{succeeds or equal to}g_{i}, for i=1, 2, ..., n? Given only the degree sequences of n graphs g_{1}, g_{2}, ..., g_{n}, is there a 3-hypergraph G whose subsumed graphs G_{1}, G_{2}, ..., G_{n} have the same degree sequences? We consider 3-hypergraphs with and without repeated edges. We prove these problems NP-complete. We indicate their relation to some well-known problems. The corresponding problems for 2-hypergraphs have simple polynomial solutions.

Original language | English (US) |
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Pages (from-to) | 239-254 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1986 |

Externally published | Yes |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete Applied Mathematics*,

*14*(3), 239-254. https://doi.org/10.1016/0166-218X(86)90028-4