A limit theorem for the six-length of random functional graphs with a fixed degree sequence

TL;DR

This paper establishes a limit theorem for the distribution of the six-length in random functional graphs with a fixed degree sequence, relevant to algorithm analysis in integer factorization.

Contribution

It provides the first limiting distribution results for the six-length in such graphs with a specified in-degree sequence.

Findings

Derived the limiting distribution of six-length

Applicable to random functional graphs with fixed degree sequences

Insights relevant to integer factorization algorithms

Abstract

We obtain results on the limiting distribution of the six-length of a random functional graph, also called a functional digraph or random mapping, with given in-degree sequence. The six-length of a vertex $v\in V$ is defined from the associated mapping, $f:V\to V$, to be the maximum $i\in V$ such that the elements $v, f(v), \ldots, f^{i-1}(v)$ are all distinct. This has relevance to the study of algorithms for integer factorisation.