### Abstract

Nontrivial lower bounds of the time complexity are given for a class of problems on graphs. Specifically, given a complete graph with weighted edges, the problem of finding a subgraph satisfying a property π and having edge‐weights that sum exactly to unity is considered. An ω(n^{3} log n) lower bound is established under the algebraic decision tree model for a property π that satisfies the degree constraint and is closed with respect to isomorphism, where n is the number of vertices in an input graph. This result is a proper generalization of that of Nakayama et al. [8], in which the same lower bound was obtained for π that is hereditary on subgraphs and determined by components. Furthermore, an ω(n^{3}) lower bound is shown for π = “clique” that does not satisfy the degree constraint and hence the above result can not be applied.

Original language | English |
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Pages (from-to) | 95-102 |

Number of pages | 8 |

Journal | Systems and Computers in Japan |

Volume | 17 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1986 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

*Systems and Computers in Japan*,

*17*(6), 95-102. https://doi.org/10.1002/scj.4690170611