### Abstract

We prove a lower bound of ω (n^{4/3} log^{1/3} n) on the randomized decision tree complexity of any nontrivial monotone n-vertex bipartite graph property, thereby improving the previous bound of ω(n ^{4/3}) due to Hajnal [H91]. Our proof works by improving a probabilistic argument in that paper, which also improves a graph packing lemma proved there. By a result of Gröger [G92] our complexity lower bound carries over from bipartite to general monotone n-vertex graph properties. Graph packing being a well-studied subject in its own right, our improved packing lemma and the probabilistic technique used to prove it, may be of independent interest.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings |

Pages | 285-296 |

Number of pages | 12 |

State | Published - Dec 1 2001 |

Event | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece Duration: Jul 8 2001 → Jul 12 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 | 2076 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 |
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Country | Greece |

City | Crete |

Period | 7/8/01 → 7/12/01 |

### Keywords

- Decision tree complexity
- Gaph packing
- Mnotone graph properties
- Pobabilistic method
- Rn-domized complexity
- Rndomized algorithms

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings*(pp. 285-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS).