Isaev, MikhailMcKay, Brendan D.Southwell, AngusZhukovskii, Maksim2025-05-232025-05-231083-6489WOS:001415005500001ORCID:/0000-0002-3553-0496/work/184023107http://www.scopus.com/inward/record.url?scp=85217547613&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733751071We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices tends to infinity. We verify this conjecture for the cases when the graphs are sufficiently dense or sparse. We also prove an asymptotic formula for the expected number of spanning regular subgraphs in a random regular graph.M. I. supported by Australian Research Council grant DP220103074. B. D. M. supported by Australian Research Council grant DP250101611.20en© 2025 The Author(s)Random regular graphsSandwich conjectureSprinkling202510.1214/25-EJP127285217547613