## Abstract

Tovey [A simplified satisfiability problem, Discrete Appl. Math. 8 (1984) 85-89] showed that it is NP-hard to decide the satisfiability of 3-SAT instances in which every variable occurs four times, while every instance of 3-SAT in which each variable occurs three times is satisfiable. We explore the border between these two problems. Answering a question of Iwama and Takaki, we show that, for every fixed k ≥ 0, there is a polynomial-time algorithm to determine the satisfiability of 3-SAT instances in which k variables occur four times and the remaining variables occur three times. On the other hand, it is NP-hard to decide the satisfiability of 3-SAT instances in which all but one variable occurs three times, and the remaining variable is allowed to occur an arbitrary number of times.

Original language | English (US) |
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Pages (from-to) | 649-653 |

Number of pages | 5 |

Journal | Discrete Applied Mathematics |

Volume | 155 |

Issue number | 5 |

DOIs | |

State | Published - Mar 15 2007 |

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics