Asymptotic enumeration of Eulerian circuits for graphs with strong mixing properties

TL;DR

This paper derives an asymptotic formula for counting Eulerian circuits in graphs with strong mixing properties and even degrees, providing precise estimates up to a small multiplicative error.

Contribution

It introduces a new asymptotic enumeration method for Eulerian circuits in strongly mixing graphs with even degrees, refining previous estimates.

Findings

Established an asymptotic formula with an error of $O(n^{-1/2+\

,

,

Abstract

We prove an asymptotic formula for the number of Eulerian circuits for graphs with strong mixing properties and with vertices having even degrees. The exact value is determined up to the multiplicative error $O(n^{-1/2+\varepsilon})$, where $n$ is the number of vertices