This article is cited in 2 papers

Asymptotic enumeration of Eulerian orientations for graphs with strong mixing properties

M. I. Isaev^ab, K. V. Isaeva<sup>ba

a</sup> Moscow Institute of Physics and Technology, 9 Institute Lane, 141700 Dolgoprudny, Russia
^b Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France

Abstract: We prove an asymptotic formula for the number of Eulerian orientations for graphs with strong mixing properties and with vertices having even degrees. The exact value is determined up to the multiplicative error $O(n^{1+\varepsilon})$, where $n$ is the number of vertices. Bibliogr. 14.

Keywords: Eulerian orientation, asymptotic analysis, Gaussian integral, algebraic connectivity, Laplacian.

UDC: 519.1

Received: 17.10.2012
Revised: 29.03.2013

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