## Abstract

The script F sign Hypergraph Sandwich Problem (script F signHSP) is introduced here as follows: Given two hypergraphs H^{1} = (X, script E sign^{1}) and H^{2} = (X, script E sign^{2}) where script E sign^{1} = {E_{1}^{1}, . . . , E_{m}^{1}}, script E sign^{2} = {E_{1}^{2}, . . . , E_{m}^{2}} and E_{i}^{1} ⊆ E_{i}^{2} for all 1 ≤ i ≤ m, is there a hypergraph H = (X, script E sign) with script E sign = {E_{1}, . . . , E_{m}} such that E_{i}^{1} ⊆ E_{i} ⊆ E_{i}^{2} for all 1 ≤ i ≤ m which belongs to a specified hypergraph family script F sign? Hypergraph sandwich problems for several properties studied here occur in a variety of important applications. We prove the NP-completeness of the Interval HSP and the Circular-arc HSP. This corresponds to the problem of deciding whether a partially specified (0,1)-valued matrix can be filled in such that the resulting 0/1 matrix has the consecutive ones property, (resp., circular ones property). The consecutive ones property arises in databases and in DNA physical mapping. Further results shown are a set of conditions relating interval hypergraphs with acyclic hypergraphs. Finally, the k-tree graph sandwich problem is studied. The general problem is shown to be NP-complete and the fixed k version is given a polynomial algorithm. Both problems are based on solutions to the corresponding partial k-tree recognition problems.

Original language | English |
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Pages (from-to) | 223-239 |

Number of pages | 17 |

Journal | Graphs and Combinatorics |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics