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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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Allen, Peter ; Bottcher, Julia ; Han, Hiep ; Kohayakawa, Yoshiharu ; Person, Yury
Total Authors: 5
Document type: Journal article
Source: COMBINATORICA; v. 37, n. 4, p. 573-616, AUG 2017.
Web of Science Citations: 2

We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph G is (epsilon,p,k,l)-pseudorandom if for all disjoint X and Y subset of V(G) with |X|>= epsilon p(n)(k) and |Y| >= epsilon p(l)n we have e(X,Y)=(1 +/-epsilon)p|X||Y|. We prove that for all beta > 0 there is an epsilon > 0 such that an (epsilon,p,1,2) -pseudorandom graph on n vertices with minimum degree at least beta pn contains the square of a Hamilton cycle. In particular, this implies that (n,d,lambda)-graphs with lambda << d(5/2)n(-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 Szabo {[}27]. We also extend our result to higher powers of Hamilton cycles and establish corresponding counting versions. (AU)

FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
Grantee:Carlos Eduardo Ferreira
Support type: Research Projects - Thematic Grants
FAPESP's process: 09/17831-7 - Embedding and packing problems in extremal graph theory
Grantee:Julia Boettcher
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 10/09555-7 - Embedding, randomised and structural problems in extremal graph theory
Grantee:Peter David Allen
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Jefferson Antonio Galves
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 10/16526-3 - Quasi-random hypergraphs and spanning subhypergraph containment
Grantee:Hiep Han
Support type: Scholarships in Brazil - Post-Doctorate