{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:51:00Z","timestamp":1781949060045,"version":"3.54.5"},"reference-count":10,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T00:00:00Z","timestamp":1781913600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T00:00:00Z","timestamp":1781913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371349"],"award-info":[{"award-number":["12371349"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LLSSZ25F030002"],"award-info":[{"award-number":["LLSSZ25F030002"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s00373-026-03051-7","type":"journal-article","created":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:08:16Z","timestamp":1781946496000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Internal Partitions of some Regular Graphs"],"prefix":"10.1007","volume":"42","author":[{"given":"Bo-Qian","family":"Zuo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ya-Hong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,20]]},"reference":[{"issue":"1","key":"3051_CR1","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1111\/1467-937X.00121","volume":"67","author":"S Morris","year":"2000","unstructured":"Morris, S.: Contagion. Rev. Econ. Stud. 67(1), 57\u201378 (2000)","journal-title":"Rev. Econ. Stud."},{"key":"3051_CR2","unstructured":"DeVos, M.: http:\/\/www.openproblemgarden.org\/op\/friendlypartitions (2009)"},{"key":"3051_CR3","first-page":"183","volume":"154","author":"KH Shafique","year":"2002","unstructured":"Shafique, K.H., Dutton, R.D.: On satisfactory partitioning of graphs. Congr. Numer. 154, 183\u2013194 (2002)","journal-title":"Congr. Numer."},{"issue":"2","key":"3051_CR4","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/S0377-2217(99)00459-2","volume":"125","author":"MU Gerber","year":"2000","unstructured":"Gerber, M.U., Kobler, D.: Algorithmic approach to the satisfactory graph partitioning problem. Eur. J. Oper. Res. 125(2), 283\u2013291 (2000)","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"3051_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1002\/jgt.21909","volume":"83","author":"A Ban","year":"2016","unstructured":"Ban, A., Linial, N.: Internal partitions of regular graphs. J. Graph Theory 83(1), 5\u201318 (2016)","journal-title":"J. Graph Theory"},{"key":"3051_CR6","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s40304-017-0114-9","volume":"5","author":"XK Tao","year":"2017","unstructured":"Tao, X.K., Liu, B.Y., Hou, X.M.: Weak internal partition of regular graphs. Commun. Math. Stat. 5, 335\u2013338 (2017)","journal-title":"Commun. Math. Stat."},{"issue":"1","key":"3051_CR7","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1002\/(SICI)1097-0118(199801)27:1<7::AID-JGT2>3.0.CO;2-U","volume":"27","author":"A Kaneko","year":"1998","unstructured":"Kaneko, A.: On decomposition of triangle free graphs under degree constraints. J. Graph Theory 27(1), 7\u20139 (1998)","journal-title":"J. Graph Theory"},{"issue":"3","key":"3051_CR8","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1002\/(SICI)1097-0118(199611)23:3<321::AID-JGT12>3.0.CO;2-H","volume":"23","author":"M Stiebitz","year":"1996","unstructured":"Stiebitz, M.: Decomposing graphs under degree constraints. J. Graph Theory 23(3), 321\u2013324 (1996)","journal-title":"J. Graph Theory"},{"key":"3051_CR9","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/j.future.2018.01.009","volume":"83","author":"WY Yang","year":"2018","unstructured":"Yang, W.Y., Wang, G.Y., Choo, K.-K.R., Chen, S.H.: HEPart: a balanced hypergraph partitioning algorithm for big data applications. Future Gener. Comput. Syst. 83, 250\u2013268 (2018)","journal-title":"Future Gener. Comput. Syst."},{"key":"3051_CR10","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s00373-024-02774-9","volume":"40","author":"P B\u00e4rnkopf","year":"2024","unstructured":"B\u00e4rnkopf, P., Nagy, Z.L., Paulovics, Z.: A note on internal partitions: the 5-regular case and beyond. Graphs Comb. 40, 36 (2024)","journal-title":"Graphs Comb."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-026-03051-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-026-03051-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-026-03051-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:08:18Z","timestamp":1781946498000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-026-03051-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,20]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["3051"],"URL":"https:\/\/doi.org\/10.1007\/s00373-026-03051-7","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,20]]},"assertion":[{"value":"17 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"58"}}