Monotone bipartite graph properties are evasive
SIAM Journal on Computing
Lower bounds on the complexity of graph properties
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the randomized complexity of monotone graph properties
Acta Cybernetica
Evasiveness of Subgraph Containment and Related Properties
SIAM Journal on Computing
Computing Graph Properties by Randomized Subcube Partitions
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Extremal Graph Theory
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We prove a lower bound of Ω(n4/3 log 1/3n) on the randomized decision tree complexity of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions of size n. This improves the previous best bound of Ω(n4/3) due to Hajnal (Combinatorica 11 (1991) 131–143). Our proof works by improving a graph packing lemma used in earlier work, and this improvement in turn stems from a novel probabilistic analysis. 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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 A shorter preliminary version of this paper appeared in the Proceedings of ICALP 2001, the 28th International Colloquium on Automata, Languages and Programming, Heraklion, Greece.