{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T13:50:08Z","timestamp":1767016208238,"version":"3.40.5"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that for every tree <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline1.png\"\/><jats:tex-math>\n$T$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> of radius <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline2.png\"\/><jats:tex-math>\n$h$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, there is an integer <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline3.png\"\/><jats:tex-math>\n$c$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that every <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline4.png\"\/><jats:tex-math>\n$T$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-minor-free graph is contained in <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline5.png\"\/><jats:tex-math>\n$H\\boxtimes K_c$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for some graph <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline6.png\"\/><jats:tex-math>\n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with pathwidth at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline7.png\"\/><jats:tex-math>\n$2h-1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000275_inline8.png\"\/><jats:tex-math>\n$2h-1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is the best possible bound.<\/jats:p>","DOI":"10.1017\/s0963548323000275","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T08:33:45Z","timestamp":1695803625000},"page":"85-90","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["The Excluded Tree Minor Theorem Revisited"],"prefix":"10.1017","volume":"33","author":[{"given":"Vida","family":"Dujmovi\u0107","sequence":"first","affiliation":[]},{"given":"Robert","family":"Hickingbotham","sequence":"additional","affiliation":[]},{"given":"Gwena\u00ebl","family":"Joret","sequence":"additional","affiliation":[]},{"given":"Piotr","family":"Micek","sequence":"additional","affiliation":[]},{"given":"Pat","family":"Morin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8866-3041","authenticated-orcid":false,"given":"David R.","family":"Wood","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,9,27]]},"reference":[{"key":"S0963548323000275_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-019-3848-z"},{"key":"S0963548323000275_ref6","unstructured":"[6] Illingworth, F. , Scott, A. and Wood, D. R. (2022). Product structure of graphs with an excluded minor. arXiv: 2104.06627."},{"key":"S0963548323000275_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90079-5"},{"key":"S0963548323000275_ref2","unstructured":"[2] Campbell, R. , Clinch, K. , Distel, M. , Gollin, J. P. , Hendrey, K. , Hickingbotham, R. , Huynh, T. , Illingworth, F. , Tamitegama, Y. , Tan, J. and Wood, D. R. (2022) Product structure of graph classes with bounded treewidth. arXiv: 2206.02395."},{"key":"S0963548323000275_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90068-U"},{"key":"S0963548323000275_ref5","doi-asserted-by":"publisher","DOI":"10.1145\/3385731"},{"key":"S0963548323000275_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001450"},{"key":"S0963548323000275_ref4","volume-title":"Graph Theory","volume":"173","author":"Diestel","year":"2018"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548323000275","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T09:49:26Z","timestamp":1703065766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548323000275\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,27]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["S0963548323000275"],"URL":"https:\/\/doi.org\/10.1017\/s0963548323000275","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2023,9,27]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}