Asymptotic enumeration of Eulerian orientations for graphs with strong mixing properties

Mikhail Isaev (1) , Isaeva Kseniia (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 MIPT - Moscow Institute of Physics and Technology [Moscow]

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+epsilon}), where n is the number of vertices.

Domaines: Combinatoire [math.CO]

Mikhail Isaev, Isaeva Kseniia. Asymptotic enumeration of Eulerian orientations for graphs with strong mixing properties. 2012. ⟨hal-00730657v1⟩