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Izvestiya: Mathematics, 2013, Volume 77, Issue 6, Pages 1105–1129
DOI: https://doi.org/10.1070/IM2013v077n06ABEH002671 (Mi im8052) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic enumeration of Eulerian circuits in graphs with strong mixing properties

M. I. Isaev

Moscow Institute of Physics and Technology
English version PDF (410 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM2013v077n06ABEH002671
Abstract: We prove an asymptotic formula for the number of Eulerian circuits in graphs with strong mixing properties and with all vertices having even degrees. This number is determined up to a multiplicative error of the form $O(n^{-1/2+\varepsilon})$, where $n$ is the number of vertices.
Keywords: Eulerian circuit, asymptotic analysis, Gaussian integral, algebraic connectivity, Laplacian matrix.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00398_а
Received: 27.09.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 6, Pages 45–70
DOI: https://doi.org/10.4213/im8052
Bibliographic databases:
Document Type: Article
UDC: 519.1
MSC: 05C30, 05C45, 41A60
Language: English
Original paper language: Russian
Citation: M. I. Isaev, “Asymptotic enumeration of Eulerian circuits in graphs with strong mixing properties”, Izv. RAN. Ser. Mat., 77:6 (2013), 45–70; Izv. Math., 77:6 (2013), 1105–1129
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2013v077n06ABEH002671
  • https://www.mathnet.ru/eng/im/v77/i6/p45
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:406
    Russian version PDF:222
    English version PDF:11
    References:42
    First page:18
     
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