### 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 |

Publisher | Springer Verlag |

Pages | 110-120 |

Number of pages | 11 |

Volume | 2010 |

ISBN (Print) | 9783540416951 |

State | Published - 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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

- Computer Science(all)
- Theoretical Computer Science

### Cite this

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

**Evasiveness of subgraph containment and related properties.** / Chakrabarti, Amit; Khot, Subhash; Shi, Yaoyun.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*STACS 2001 - 18th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings.*vol. 2010, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2010, Springer Verlag, pp. 110-120, 18th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2001, Dresden, Germany, 2/15/01.

}

TY - GEN

T1 - Evasiveness of subgraph containment and related properties

AU - Chakrabarti, Amit

AU - Khot, Subhash

AU - Shi, Yaoyun

PY - 2001

Y1 - 2001

N2 - 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 ½n2 − 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.

AB - 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 ½n2 − 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.

KW - Decision tree complexity

KW - Evasiveness

KW - Graph property testing

KW - Monotone graph properties

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UR - http://www.scopus.com/inward/citedby.url?scp=84957090550&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84957090550

SN - 9783540416951

VL - 2010

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 110

EP - 120

BT - STACS 2001 - 18th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

PB - Springer Verlag

ER -