[{"language":[{"iso":"eng"}],"status":"public","date_published":"2026-10-01T00:00:00Z","acknowledgement":"We are grateful to Béla Bollobás, to Matthew Kwan and to Fabio\r\nToninelli for their helpful comments and suggestions, and to Nicholas Wormald for useful\r\nremarks on a preliminary version of this work and pointing us towards the reference [29].\r\nThe authors would also like to thank several anonymous referees for many useful suggestions,\r\nincluding pointing out that Lemma 2.10 already appeared in [11].\r\nPart of this research was done during a visit of the fourth author to IST Austria. We thank\r\nIST Austria for its hospitality.\r\nFor open access purposes, the authors have applied a CC BY public copyright license to\r\nany author accepted manuscript version arising from this submission. L. Hollom was supported by the Internal Graduate Studentship of Trinity College, Cambridge.\r\nL. Lichev was supported by the Austrian Science Fund (FWF) grant No. 10.55776/ESP624.\r\nA. Mond was supported by UK Research and Innovation grant MR/W007320/2. Wang was\r\nsupported by the ERC Starting Grant “RANDSTRUCT” No. 101076777.","department":[{"_id":"MaKw"},{"_id":"GradSch"}],"scopus_import":"1","arxiv":1,"supplementarymaterial":"no","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"PlanS_conform":"1","issue":"5","fulldoi":"https://doi.org/10.1214/26-AAP2345","publication_status":"published","has_accepted_license":"1","publisher":"Institute of Mathematical Statistics","file":[{"content_type":"application/pdf","date_updated":"2026-10-19T07:33:58Z","relation":"main_file","file_size":320593,"checksum":"46101e61d29cf40f0a204801d15a848f","file_id":"23165","access_level":"open_access","file_name":"2026_AnnalsAppliedProbability_Hollom.pdf","success":1,"date_created":"2026-10-19T07:33:58Z","creator":"dernst"}],"external_id":{"arxiv":["2505.22875"]},"month":"10","_id":"23155","publication_identifier":{"eissn":["2168-8737"],"issn":["1050-5164"]},"abstract":[{"text":"In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we\r\nshow that, for a wide range of parameters d1 ≤ d2, there exists a coupling of\r\nG(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.\r\nOur contributions include new tools for analysing contiguity and total variation distance between random regular graph models, a novel procedure for\r\ngenerating 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,\r\nMcKay, Southwell and Zhukovskii.","lang":"eng"}],"OA_type":"hybrid","date_created":"2026-10-18T22:01:52Z","year":"2026","day":"01","article_type":"original","page":"4716-4738","citation":{"ieee":"L. Hollom, L. Lichev, A. Mond, J. Portier, and Y. Wang, “Monotonicity and decompositions of random regular graphs,” <i>Annals of Applied Probability</i>, vol. 36, no. 5. Institute of Mathematical Statistics, pp. 4716–4738, 2026.","mla":"Hollom, Lawrence, et al. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>, vol. 36, no. 5, Institute of Mathematical Statistics, 2026, pp. 4716–38, doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>.","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Y. Wang, Annals of Applied Probability 36 (2026) 4716–4738.","chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, Julien Portier, and Yiting Wang. “Monotonicity and Decompositions of Random Regular Graphs.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>.","ista":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. 2026. Monotonicity and decompositions of random regular graphs. Annals of Applied Probability. 36(5), 4716–4738.","ama":"Hollom L, Lichev L, Mond A, Portier J, Wang Y. Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. 2026;36(5):4716-4738. doi:<a href=\"https://doi.org/10.1214/26-AAP2345\">10.1214/26-AAP2345</a>","apa":"Hollom, L., Lichev, L., Mond, A., Portier, J., &#38; Wang, Y. (2026). Monotonicity and decompositions of random regular graphs. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/26-AAP2345\">https://doi.org/10.1214/26-AAP2345</a>"},"doi":"10.1214/26-AAP2345","keyword":["Random regular graphs","coupling","contiguity","total variation distance","decomposition"],"project":[{"name":"Randomness and structure in combinatorics","grant_number":"101076777","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"},{"grant_number":"E624","name":"THRESHOLDS IN SEMI-RANDOM PROCESSES AND GRAPH EMBEDDINGS","_id":"e19fef4c-1f3d-11f0-ac04-b8b1af6886d8"}],"intvolume":"        36","oa":1,"quality_controlled":"1","oa_version":"Published Version","das_tickbox":"0","date_updated":"2026-10-19T07:39:17Z","researchdata_availability":"no","mathsc":["05C80"],"file_date_updated":"2026-10-19T07:33:58Z","OA_place":"publisher","article_processing_charge":"Yes (in subscription journal)","title":"Monotonicity and decompositions of random regular graphs","author":[{"full_name":"Hollom, Lawrence","first_name":"Lawrence","last_name":"Hollom"},{"full_name":"Lichev, Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","first_name":"Lyuben","last_name":"Lichev"},{"first_name":"Adva","last_name":"Mond","full_name":"Mond, Adva"},{"last_name":"Portier","first_name":"Julien","full_name":"Portier, Julien"},{"id":"1917d194-076e-11ed-97cd-837255f88785","full_name":"Wang, Yiting","first_name":"Yiting","last_name":"Wang"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","volume":36,"publication":"Annals of Applied Probability","ddc":["500"]}]