Geodesic
Asymptotic enumeration of Eulerian circuits in graphs with strong mixing properties
Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1105-1129

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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: asymptotic analysis, Gaussian integral, algebraic connectivity
Mots-clés : Eulerian circuit, Laplacian matrix. 
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     author = {M. I. Isaev},
     title = {Asymptotic enumeration of {Eulerian} circuits in graphs with strong mixing properties},
     journal = {Izvestiya. Mathematics },
     pages = {1105--1129},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a1/}
}
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M. I. Isaev. Asymptotic enumeration of Eulerian circuits in graphs with strong mixing properties. Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1105-1129. http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a1/