### Abstract

We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks and Sturtevant [4]. For the property of containing a subgraph isomorphic to a fixed graph, and a fairly large class of related n-vertex graph properties, we show evasiveness for an arithmetic progression of values of n. This implies a ½n^{2} − O(n) lower bound on the decision tree complexity of these properties. We prove that properties that are preserved under taking graph minors are evasive for all sufficiently large n. This greatly generalizes the evasiveness result for planarity [1]. We prove a similar result for bipartite subgraph containment.

Original language | English (US) |
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Title of host publication | STACS 2001 - 18th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings |

Editors | Afonso Ferreira, Horst Reichel |

Publisher | Springer Verlag |

Pages | 110-120 |

Number of pages | 11 |

ISBN (Print) | 9783540416951 |

State | Published - Jan 1 2001 |

Event | 18th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2001 - Dresden, Germany Duration: Feb 15 2001 → Feb 17 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2010 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2001 |
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Country | Germany |

City | Dresden |

Period | 2/15/01 → 2/17/01 |

### Fingerprint

### Keywords

- Decision tree complexity
- Evasiveness
- Graph property testing
- Monotone graph properties

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*STACS 2001 - 18th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings*(pp. 110-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2010). Springer Verlag.