The Annals of Applied Probability· 2026Q1
Monotonicity and decompositions of random regular graphs
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- Q1SCImago
- 2026year
Short summary
For a wide range of parameters d1≤d2, a coupling of random regular graphs G(n,d1) and G(n,d2) exists such that G(n,d1) is a subgraph of G(n,d2) with high probability, confirming a conjecture.
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Key points
- A coupling of G(n,d1) and G(n,d2) exists such that G(n,d1)⊆G(n,d2) with high probability for d1≤d2.
- Confirms a conjecture by Gao, Isaev, and McKay in a new parameter regime.
- Introduces new analytical tools for contiguity and total variation distance between random graph models.
- Presents a novel procedure for generating unions of random edge-disjoint perfect matchings.
- Refines estimates of Gao's bounds on the number of perfect matchings in random regular graphs.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameters d1≤d2, there exists a coupling of G(n,d1) and G(n,d2) satisfying that G(n,d1)⊆G(n,d2) with high probability, confirming a conjecture of Gao, Isaev and McKay in a new regime. Our contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for generating unions of random edge-disjoint perfect matchings, and refined estimates of Gao’s bounds on the number of perfect matchings in random regular graphs. In addition, we make progress towards another conjecture of Isaev, McKay, Southwell and Zhukovskii.
The authors' abstract, as published at the source. The Annals of Applied Probability, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics