Library Header Image
LSE Research Online LSE Library Services

Powers of hamilton cycles in pseudorandom graphs

Allen, Peter, Böttcher, Julia, Hàn, Hiệp, Kohayakawa, Yoshiharu and Person, Yury (2014) Powers of hamilton cycles in pseudorandom graphs. LATIN 2014: Theoretical Informatics, 8392 (30). pp. 355-366. ISSN 1611-3349

Full text not available from this repository.

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


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:
Additional Information: © 2014 Springer-Verlag Berlin Heidelberg
Divisions: Mathematics
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: 20 Feb 2021 05:15

Actions (login required)

View Item View Item