## Abstract

The graph sandwich problem for property ⊆ is defined as follows: Given two graphs G^{1} = (V, E^{1}) and G^{2} = (V, E^{2}) such that E^{1} ⊆ E^{2}, is there a graph G = (V, E) such that E^{1} ⊆ E ⊆ E^{2} which satisfies property ⊆? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NP-completeness of others. We describe polynomial time algorithms for threshold graphs, split graphs, and cographs. For the sandwich problem for threshold graphs, the only case in which a previous algorithm existed, we obtain a faster algorithm. NP-completeness proofs are given for comparability graphs, permutation graphs, and several other families. For Eulerian graphs; one Version of the problem is polynomial and another is NP-complete.

Original language | English |
---|---|

Pages (from-to) | 449-473 |

Number of pages | 25 |

Journal | Journal of Algorithms |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1995 |

Externally published | Yes |

## ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics