{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T14:20:25Z","timestamp":1775830825393,"version":"3.50.1"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T00:00:00Z","timestamp":1355961600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>We study the number of edge-disjoint Hamilton cycles one can guarantee in a sufficiently large graph <jats:italic>G<\/jats:italic> on <jats:italic>n<\/jats:italic> vertices with minimum degree \u03b4=(1\/2+\u03b1)<jats:italic>n<\/jats:italic>. For any constant \u03b1&gt;0, we give an optimal answer in the following sense: let reg<jats:sub>even<\/jats:sub>(<jats:italic>n<\/jats:italic>,\u03b4) denote the degree of the largest even-regular spanning subgraph one can guarantee in a graph on <jats:italic>n<\/jats:italic> vertices with minimum degree \u03b4. Then the number of edge-disjoint Hamilton cycles we find equals reg<jats:sub>even<\/jats:sub>(<jats:italic>n<\/jats:italic>,\u03b4)\/2. The value of reg<jats:sub>even<\/jats:sub>(<jats:italic>n<\/jats:italic>,\u03b4) is known for infinitely many values of <jats:italic>n<\/jats:italic> and \u03b4. We also extend our results to graphs <jats:italic>G<\/jats:italic> of minimum degree \u03b4 \u2265 <jats:italic>n<\/jats:italic>\/2, unless <jats:italic>G<\/jats:italic> is close to the extremal constructions for Dirac's theorem. Our proof relies on a recent and very general result of K\u00fchn and Osthus on Hamilton decomposition of robustly expanding regular graphs.<\/jats:p>","DOI":"10.1017\/s0963548312000569","type":"journal-article","created":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T13:11:52Z","timestamp":1356009112000},"page":"394-416","source":"Crossref","is-referenced-by-count":16,"title":["Optimal Packings of Hamilton Cycles in Graphs of High Minimum Degree"],"prefix":"10.1017","volume":"22","author":[{"given":"DANIELA","family":"K\u00dcHN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOHN","family":"LAPINSKAS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DERYK","family":"OSTHUS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,12,20]]},"reference":[{"key":"S0963548312000569_ref4","unstructured":"Hartke S. G. , Martin R. and Seacrest T. Relating minimum degree and the existence of a k-factor. Research manuscript."},{"key":"S0963548312000569_ref3","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548312000569_ref10","doi-asserted-by":"publisher","DOI":"10.1137\/110849171"},{"key":"S0963548312000569_ref11","unstructured":"K\u00fchn D. and Osthus D. Hamilton decompositions of regular expanders: A proof of Kelly's conjecture for large tournaments. Preprint."},{"key":"S0963548312000569_ref5","unstructured":"Hartke S. G. and Seacrest T. Random partitions and edge-disjoint Hamiltonian cycles. Preprint."},{"key":"S0963548312000569_ref14","first-page":"813","volume-title":"Combinatorial Theory and its Applications III: Proc. Colloq., Balatonf\u00fcred, 1969","author":"Nash-Williams","year":"1970"},{"key":"S0963548312000569_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.10.005"},{"key":"S0963548312000569_ref2","unstructured":"Csaba B. , K\u00fchn D. , Lo A. , Osthus D. and Treglown A. Personal communication."},{"key":"S0963548312000569_ref7","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-19.1.13"},{"key":"S0963548312000569_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02880991"},{"key":"S0963548312000569_ref12","unstructured":"K\u00fchn D. and Osthus D. Hamilton decompositions of regular expanders: applications. Preprint."},{"key":"S0963548312000569_ref9","unstructured":"Knox F. , K\u00fchn D. and Osthus D. Edge-disjoint Hamilton cycles in random graphs. Preprint."},{"key":"S0963548312000569_ref17","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1952-028-2"},{"key":"S0963548312000569_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.11.004"},{"key":"S0963548312000569_ref15","first-page":"157","volume-title":"Studies in Pure Mathematics (Presented to Richard Rado","author":"Nash-Williams","year":"1971"},{"key":"S0963548312000569_ref6","unstructured":"Hefetz D. , K\u00fchn D. , Lapinskas J. and Osthus D. Optimal covers with Hamilton cycles in random graphs. Preprint."},{"key":"S0963548312000569_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059438"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548312000569","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T22:01:16Z","timestamp":1556056876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548312000569\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,20]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["S0963548312000569"],"URL":"https:\/\/doi.org\/10.1017\/s0963548312000569","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,20]]}}}