Thesis
Partitions of random graphs, invertibility of digraphs and the Erdős-Rothschild problem
- Abstract:
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We begin by studying the number of partitions satisfying degree congruence conditions in random graphs. For G = Gn,1/2, the Erdős–Renyi random graph, let Xn be the random variable representing the number of distinct partitions of V (G) into sets A1, . . . , Aq so that the degree of each vertex in G[Ai ] is divisible by q for all i ∈ [q]. We prove that if q ⩾ 3 is odd then Xn d −→ Po(1/q!), and if q ⩾ 4 is even then Xn d −→ Po(2q/q!). More generally, we show that the distribution is still asym...
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- Files:
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(Preview, Dissemination version, pdf, 2.3MB, Terms of use)
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Authors
Contributors
+ Scott, A
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Mathematical Institute
- Role:
- Supervisor
- ORCID:
- 0000-0003-4489-5988
+ McDiarmid, C
- Institution:
- University of Oxford
- Division:
- MPLS
- Department:
- Statistics
- Role:
- Examiner
- ORCID:
- 0000-0001-8111-623X
+ Pikhurko, O
- Role:
- Examiner
+ Engineering and Physical Sciences Research Council
More from this funder
- Funder identifier:
- https://ror.org/0439y7842
- Funding agency for:
- Powierski, E
- Type of award:
- DPhil
- Level of award:
- Doctoral
- Awarding institution:
- University of Oxford
- Language:
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English
- Subjects:
- Deposit date:
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2026-05-14
- ARK identifier:
Terms of use
- Copyright holder:
- Emil Powierski
- Copyright date:
- 2025
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