{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T22:21:04Z","timestamp":1783722064868,"version":"3.55.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T00:00:00Z","timestamp":1715990400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T00:00:00Z","timestamp":1715990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["NSTC-111-2115-M-004-002-MY2"],"award-info":[{"award-number":["NSTC-111-2115-M-004-002-MY2"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2024,7]]},"DOI":"10.1007\/s11538-024-01309-w","type":"journal-article","created":{"date-parts":[[2024,5,18]],"date-time":"2024-05-18T18:01:32Z","timestamp":1716055292000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Counting Phylogenetic Networks with Few Reticulation Vertices: Galled and Reticulation-Visible Networks"],"prefix":"10.1007","volume":"86","author":[{"given":"Yu-Sheng","family":"Chang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8891-6897","authenticated-orcid":false,"given":"Michael","family":"Fuchs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,18]]},"reference":[{"key":"1309_CR1","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.aam.2016.04.004","volume":"78","author":"M Bordewich","year":"2016","unstructured":"Bordewich M, Semple C (2016) Reticulation-visible networks. Adv Appl Math 78:114\u2013141","journal-title":"Adv Appl Math"},{"key":"1309_CR2","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.jcss.2020.06.001","volume":"114","author":"G Cardona","year":"2020","unstructured":"Cardona G, Zhang L (2020) Counting and enumerating tree-child networks and their subclasses. J Comput Syst Sci 114:84\u2013104","journal-title":"J Comput Syst Sci"},{"key":"1309_CR3","unstructured":"Chang Y-S, Fuchs M, Liu H, Wallner M, Yu G-R (2022a) Enumeration of $$d$$-combining tree-child networks, LIPICS. In: Proceedings of the 33rd meeting on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms, vol 225. p 5"},{"key":"1309_CR4","doi-asserted-by":"crossref","unstructured":"Chang Y-S, Fuchs M, Liu H, Wallner M, Yu G-R (2022b) Enumerative and distributional results for $$d$$-combining tree-child networks. Adv Appl Math 157:102704","DOI":"10.1016\/j.aam.2024.102704"},{"key":"1309_CR5","unstructured":"Chang Y-S, Fuchs M, Yu G-R (2024) Galled tree-child networks, LIPICS. In: Proceedings of the 35th meeting on probabilistic, combinatorial and asymptotic methods for the analysis of algorithms, vol 302. p 2"},{"key":"1309_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655","volume-title":"Analytic combinatorics","author":"P Flajolet","year":"2009","unstructured":"Flajolet P, Sedgewick R (2009) Analytic combinatorics, 1st edn. Cambridge University Press, Cambridge","edition":"1"},{"issue":"2","key":"1309_CR7","first-page":"385","volume":"73","author":"M Fuchs","year":"2019","unstructured":"Fuchs M, Gittenberger B, Mansouri M (2019) Counting phylogenetic networks with few reticulation vertices: tree-child and normal networks. Australas J Combin 73(2):385\u2013423","journal-title":"Australas J Combin"},{"issue":"2","key":"1309_CR8","first-page":"257","volume":"82","author":"M Fuchs","year":"2021","unstructured":"Fuchs M, Gittenberger B, Mansouri M (2021) Counting phylogenetic networks with few reticulation vertices: exact enumeration and corrections. Australas J Combin 82(2):257\u2013282","journal-title":"Australas J Combin"},{"key":"1309_CR9","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.dam.2022.03.026","volume":"320","author":"M Fuchs","year":"2022","unstructured":"Fuchs M, Huang E-Y, Yu G-R (2022) Counting phylogenetic networks with few reticulation vertices: a second approach. Discrete Appl Math 320:140\u2013149","journal-title":"Discrete Appl Math"},{"key":"1309_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2020.103278","volume":"93","author":"M Fuchs","year":"2021","unstructured":"Fuchs M, Yu G-R, Zhang L (2021) On the asymptotic growth of the number of tree-child networks. Euro J Combin 93:103278","journal-title":"Euro J Combin"},{"key":"1309_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2022.105599","volume":"189","author":"M Fuchs","year":"2022","unstructured":"Fuchs M, Yu G-R, Zhang L (2022) Asymptotic enumeration and distributional properties of galled networks. J Comb Theory Ser A 189:105599","journal-title":"J Comb Theory Ser A"},{"key":"1309_CR12","doi-asserted-by":"crossref","unstructured":"Gambette P, Gunawan ADM, Labarre A, Vialette S, Zhang L (2015) Locating a tree in a phylogenetic network in quadratic time, In: Proc. of the 19th Int\u2019l Conf. Res. in Comput. Mol. Biol. (RECOMB), Warsaw, pp 96\u2013107","DOI":"10.1007\/978-3-319-16706-0_12"},{"key":"1309_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/j.ic.2016.11.001","volume":"252","author":"ADM Gunawan","year":"2017","unstructured":"Gunawan ADM, DasGupta B, Zhang L (2017) A decomposition theorem and two algorithms for reticulation-visible networks. Inf Comput 252:161\u2013175","journal-title":"Inf Comput"},{"key":"1309_CR14","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/j.dam.2020.03.005","volume":"283","author":"ADM Gunawan","year":"2020","unstructured":"Gunawan ADM, Rathin J, Zhang L (2020) Counting and enumerating galled networks. Discrete Appl Math 283:644\u2013654","journal-title":"Discrete Appl Math"},{"issue":"3","key":"1309_CR15","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1089\/cmb.2018.0220","volume":"26","author":"ADM Gunawan","year":"2019","unstructured":"Gunawan ADM, Yan H, Zhang L (2019) Compression of phylogenetic networks and algorithm for the tree containment problem. J Comput Biol 26(3):285\u2013294","journal-title":"J Comput Biol"},{"key":"1309_CR16","unstructured":"Gunawan ADM, Zhang L (2015) Bounding the size of a network defined by visibility property, arXiv:1510.00115"},{"key":"1309_CR17","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00285-022-01746-y","volume":"84","author":"S Kong","year":"2022","unstructured":"Kong S, Pons JC, Kubatko L, Wicke K (2022) Classes of explicit phylogenetic networks and their biological and mathematical significance. J Math Biol 84:47","journal-title":"J Math Biol"},{"key":"1309_CR18","first-page":"40","volume":"83","author":"M Mansouri","year":"2022","unstructured":"Mansouri M (2022) Counting general phylogenetic networks. Australas J Combin 83:40\u201386","journal-title":"Australas J Combin"},{"issue":"2","key":"1309_CR19","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/s11538-009-9449-z","volume":"72","author":"SJ Willson","year":"2010","unstructured":"Willson SJ (2010) Properties of normal phylogenetic networks. Bull Math Biol 72(2):340\u2013358","journal-title":"Bull Math Biol"},{"key":"1309_CR20","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1186\/s12859-019-3209-3","volume":"20","author":"L Zhang","year":"2019","unstructured":"Zhang L (2019) Generating normal networks via leaf insertion and nearest neighbor interchange. BMC Bioinform 20:642","journal-title":"BMC Bioinform"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-024-01309-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11538-024-01309-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-024-01309-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T09:25:16Z","timestamp":1719221116000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11538-024-01309-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,18]]},"references-count":20,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["1309"],"URL":"https:\/\/doi.org\/10.1007\/s11538-024-01309-w","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,18]]},"assertion":[{"value":"16 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"76"}}