{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T15:49:07Z","timestamp":1775749747564,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005711","name":"Universit\u00e4t Hamburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2025,12]]},"abstract":"Abstract<\/jats:title>\n \n We prove that there is a function\n f<\/jats:italic>\n such that every graph with no\n K<\/jats:italic>\n -fat\n \n \n $$K_4$$<\/jats:tex-math>\n \n \n K<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n minor is\n f<\/jats:italic>\n (\n K<\/jats:italic>\n )-quasi-isometric to a graph with no\n \n \n $$K_4$$<\/jats:tex-math>\n \n \n K<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n minor. This solves the\u00a0\n \n \n $$K_4$$<\/jats:tex-math>\n \n \n K<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -case of a general conjecture of Georgakopoulos and Papasoglu. Our proof technique also yields a new short proof of the respective\u00a0\n \n \n $$K_4^-$$<\/jats:tex-math>\n \n \n K<\/mml:mi>\n 4<\/mml:mn>\n -<\/mml:mo>\n <\/mml:msubsup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -case, which was first established by Fujiwara and Papasoglu.\n <\/jats:p>","DOI":"10.1007\/s00493-025-00189-5","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T12:04:13Z","timestamp":1762517053000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Characterisation of Graphs Quasi-isometric to $$K_4$$-minor-free Graphs"],"prefix":"10.1007","volume":"45","author":[{"given":"Sandra","family":"Albrechtsen","sequence":"first","affiliation":[]},{"given":"Raphael W.","family":"Jacobs","sequence":"additional","affiliation":[]},{"given":"Paul","family":"Knappe","sequence":"additional","affiliation":[]},{"given":"Paul","family":"Wollan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"key":"189_CR1","unstructured":"Abrishami, T., Jacobs, R.W., Knappe, P., Kobler, J.: Locally chordal graphs, (2025), arXiv preprint, arXiv:2501.17320,"},{"key":"189_CR2","unstructured":"Albrechtsen, Sandra, Diestel, Reinhard, Elm, Ann-Kathrin, Fluck, Eva, Jacobs, Raphael\u00a0W., Knappe, Paul, Wollan, Paul: A structural duality for path-decompositions into parts of small radius, (2023), arXiv preprint, arXiv:2307.08497v2,"},{"issue":"2","key":"189_CR3","doi-asserted-by":"publisher","first-page":"1438","DOI":"10.1137\/23M1573082","volume":"38","author":"Sandra Albrechtsen","year":"2024","unstructured":"Albrechtsen, Sandra, Huynh, Tony, Jacobs, Raphael W., Knappe, Paul, Wollan, Paul: A Menger-type theorem for two induced paths. 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