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- Title
A scaling limit for the length of the longest cycle in a sparse random digraph.
- Authors
Anastos, Michael; Frieze, Alan
- Abstract
We discuss the length L→c,n of the longest directed cycle in the sparse random digraph Dn,p,p=c/n, c constant. We show that for large c there exists a function f→(c) such that L→c,n/n→f→(c) a.s. The function f→(c)=1−∑k=1∞pk(c)e−kc where pk is a polynomial in c. We are only able to explicitly give the values p1,p2, although we could in principle compute any pk.
- Subjects
POLYNOMIALS
- Publication
Random Structures & Algorithms, 2022, Vol 60, Issue 1, p3
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.21030