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Powers of hamilton cycles in pseudorandom graphs

Allen, Peter and Böttcher, Julia and Hàn, Hiệp and Kohayakawa, Yoshiharu and Person, Yury (2014) Powers of hamilton cycles in pseudorandom graphs. LATIN 2014: Theoretical Informatics, 8392 (30). pp. 355-366. ISSN 16113349

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Identification Number: 10.1007/978-3-642-54423-1_31

Abstract

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph G is (ε, p, k, ℓ)-pseudorandom if for all disjoint X, Y ⊆ V (G) with /X/ ≥ εpkn and |Y| ≥ εpℓn we have e(X, Y ) = (1 ± ε)p/X//Y/. We prove that for all β > 0 there is an ε > 0 such that an (ε, p, 1, 2)-pseudorandom graph on n vertices with minimum degree at least βpn contains the square of a Hamilton cycle. In particular, this implies that (n, d, λ)-graphs with λ ≫ d5/2n?3/2 contain the square of a Hamilton cycle, and thus a triangle factor if n is a multiple of 3. This improves on a result of Krivelevich, Sudakov and Szabó [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), no. 3, 403- 426]. We also obtain results for higher powers of Hamilton cycles and establish corresponding counting versions. Our proofs are constructive, and yield deterministic polynomial time algorithms.

Item Type: Article
Official URL: http://www.springer.com/computer/theoretical+compu...
Additional Information: © 2014 Springer-Verlag Berlin Heidelberg
Subjects: G Geography. Anthropology. Recreation > GA Mathematical geography. Cartography
JEL classification: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Sets: Departments > Mathematics
Date Deposited: 09 Jun 2014 16:09
Last Modified: 04 May 2017 14:44
URI: http://eprints.lse.ac.uk/id/eprint/56949

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