### Abstract

We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297-306]. 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 1/2n^{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 a theorem due to Best, van Emde Boas, and Lenstra [A Sharpened Version of the Aanderaa-Rosenberg Conjecture, Report ZW 30/74, Mathematisch Centrum, Amsterdam, The Netherlands, 1974] which states that planarity is evasive. We prove a similar result for bipartite subgraph containment.

Original language | English (US) |
---|---|

Pages (from-to) | 866-875 |

Number of pages | 10 |

Journal | SIAM Journal on Computing |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - 2002 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*31*(3), 866-875. https://doi.org/10.1137/S0097539700382005

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

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 31, no. 3, pp. 866-875. https://doi.org/10.1137/S0097539700382005

}

TY - JOUR

T1 - Evasiveness of subgraph containment and related properties

AU - Chakrabarti, Amit

AU - Khot, Subhash

AU - Shi, Yaoyun

PY - 2002

Y1 - 2002

N2 - We prove new results on evasiveness of monotone graph properties by extending the techniques of Kahn, Saks, and Sturtevant [Combinatorica, 4 (1984), pp. 297-306]. 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 1/2n2 - 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 a theorem due to Best, van Emde Boas, and Lenstra [A Sharpened Version of the Aanderaa-Rosenberg Conjecture, Report ZW 30/74, Mathematisch Centrum, Amsterdam, The Netherlands, 1974] which states that planarity is evasive. 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 [Combinatorica, 4 (1984), pp. 297-306]. 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 1/2n2 - 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 a theorem due to Best, van Emde Boas, and Lenstra [A Sharpened Version of the Aanderaa-Rosenberg Conjecture, Report ZW 30/74, Mathematisch Centrum, Amsterdam, The Netherlands, 1974] which states that planarity is evasive. We prove a similar result for bipartite subgraph containment.

KW - Decision tree complexity

KW - Evasiveness

KW - Graph property testing

KW - Monotone graph properties

KW - Topological method

UR - http://www.scopus.com/inward/record.url?scp=0036304372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036304372&partnerID=8YFLogxK

U2 - 10.1137/S0097539700382005

DO - 10.1137/S0097539700382005

M3 - Article

VL - 31

SP - 866

EP - 875

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 3

ER -