Powers of Hamilton cycles in pseudorandom graphs
type: Item
instance of: scholarly article
title: Powers of Hamilton cycles in pseudorandom graphs
zbMATH Open document ID: 1399.05118
author: Juan-Miguel Gracia
published in: Combinatorica
publication date: 2018-02-12T00:00:00Z
full work available at URL: Powers of Hamilton cycles in pseudorandom graphs1.pdf
review text: In this paper, the authors study the appearance of Hamiltonian cycles in pseudorandom graphs. The work is structured into six sections. In Section 1, pseudorandom graphs are presented, a summary of the authors' results and of other authors' results are mentioned. The authors give some basic definitions, outline their proof strategy, provide the main lemmas and prove the main theorem (Theorem 2) in Section 2. In Section 3 and 4, the authors prove their 3 main lemmas. In Section 5, they present how to modify the proof of Theorem 2 to get Theorem 5 (the authors obtain a count close, which is the expected number of labeled copies of the \(k\)-th power of a Hamiltonian cycle in pseudorandom graphs). In the last section, they make some final remarks and present some open problems.
reviewed by: Eleonor Ciurea
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 6837301
zbMATH Keywords: extremal problems
zbMATH Keywords: asymptotic enumeration
zbMATH Keywords: Hamiltonian cycles
zbMATH Keywords: pseudorandom graphs
Wikidata QID: Q101496264
MaRDI profile type: Publication
OpenAlex ID: W2110787567
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DOI: 10.1007/S00493-015-3228-2
description: scientific article; zbMATH DE number 6837301