Journal article
Counting partitions of Gn,1/2 with degree congruence conditions
- Abstract:
- For (Formula presented.), the Erdős–Renyi random graph, let (Formula presented.) be the random variable representing the number of distinct partitions of (Formula presented.) into sets (Formula presented.) so that the degree of each vertex in (Formula presented.) is divisible by (Formula presented.) for all (Formula presented.). We prove that if (Formula presented.) is odd then (Formula presented.), and if (Formula presented.) is even then (Formula presented.). More generally, we show that the distribution is still asymptotically Poisson when we require all degrees in (Formula presented.) to be congruent to (Formula presented.) modulo (Formula presented.) for each (Formula presented.), where the residues (Formula presented.) may be chosen freely. For (Formula presented.), the distribution is not asymptotically Poisson, but it can be determined explicitly.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Version of record, pdf, 1.3MB, Terms of use)
-
- Publisher copy:
- 10.1002/rsa.21115
Authors
+ Engineering and Physical Sciences Research Council
More from this funder
- Funder identifier:
- https://ror.org/0439y7842
- Grant:
- R11443
- Publisher:
- Wiley
- Journal:
- Random Structures and Algorithms More from this journal
- Volume:
- 62
- Issue:
- 3
- Pages:
- 564-584
- Publication date:
- 2022-10-02
- Acceptance date:
- 2021-12-06
- DOI:
- EISSN:
-
1098-2418
- ISSN:
-
1042-9832
- Language:
-
English
- Keywords:
- Pubs id:
-
1285720
- Local pid:
-
pubs:1285720
- Deposit date:
-
2025-03-26
- ARK identifier:
Terms of use
- Copyright holder:
- Balister et al.
- Copyright date:
- 2022
- Rights statement:
- © 2022 The Authors. Random Structures & Algorithms published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
If you are the owner of this record, you can report an update to it here: Report update to this record