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Matematicheskie Zametki, 2013, Volume 93, Issue 6, Pages 828–843
DOI: https://doi.org/10.4213/mzm9249 (Mi mzm9249) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic Behavior of the Number of Eulerian Orientations of Graphs

M. I. Isaevab

a Centre de Mathématiques Appliquées, École Polytechnique
b Moscow Institute of Physics and Technology (State University)
Full-text PDF (559 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm9249
Abstract: The class of simple graphs with large algebraic connectivity (the second minimal eigenvalue of the Laplacian matrix) is considered. For graphs of this class, the asymptotic behavior of the number of Eulerian orientations is obtained. New properties of the Laplacian matrix are established, as well as an estimate of the conditioning of matrices with asymptotic diagonal dominance is obtained.
Keywords: simple graph, Eulerian orientation of a graph, algebraic connectivity, Laplacian matrix, matrix with diagonal dominance, spanning tree, conditioning of a matrix.
Received: 03.09.2011
Revised: 21.04.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 6, Pages 816–829
DOI: https://doi.org/10.1134/S0001434613050210
Bibliographic databases:
Document Type: Article
UDC: 519.175
Language: Russian
Citation: M. I. Isaev, “Asymptotic Behavior of the Number of Eulerian Orientations of Graphs”, Mat. Zametki, 93:6 (2013), 828–843; Math. Notes, 93:6 (2013), 816–829
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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