Asymptotic behaviour of the number of the Eulerian circuits

Mikhail Isaev (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We determine the asymptotic behaviour of the number of the Eulerian circuits in undirected simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). We also prove some new properties of the Laplacian matrix.

Mots clés: Eulirian circuits; Laplacian matrix; algebraic connectivity

Domaines: Combinatoire [math.CO]

Mikhail Isaev. Asymptotic behaviour of the number of the Eulerian circuits. The Electronic Journal of Combinatorics, 2011, 18 (1), pp.219. ⟨hal-00586307v3⟩