An Ω(n ^{4/3} ) lower bound on the randomized complexity of graph properties Authors Péter Hajnal Department of Computer Science Princeton University Bolyai Institute University of Szeged Article

Received: 03 May 1988 Revised: 02 January 1990 DOI :
10.1007/BF01206357

Cite this article as: Hajnal, P. Combinatorica (1991) 11: 131. doi:10.1007/BF01206357
Abstract We improve King's Ω(n ^{5/4} ) lower bound on the randomized decision tree complexity of monotone graph properties to Ω(n ^{4/3} ). The proof follows Yao's approach and improves it in a different direction from King's. At the heart of the proof are a duality argument combined with a new packing lemma for bipartite graphs.

AMS subject classification code (1980) 68 Q 15 05 C 35 05 C 80 The paper was written while the author was a graduate student at the University of Chicago and was completed at M.I.T. The work was supported in part by NSF under GRANT number NSF 5-27561, the Air Force under Contract OSR-86-0076 and by DIMACS (Center for Discret Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center-NSF-STC88-09648.

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