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

Kevin Leckey, Nicholas Wormald

Research output: Contribution to journalArticleResearchpeer-review


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∈V  is defined from the associated mapping, f:V→V, to be the maximum integer i  such that the elements v, f(v),…,fi−1(v) are all distinct. This has relevance to the study of algorithms for integer factorisation.

Original languageEnglish
Article numberP4.35
Number of pages17
JournalElectronic Journal of Combinatorics
Issue number4
Publication statusPublished - 22 Nov 2019

Cite this