{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T05:25:00Z","timestamp":1740461100189,"version":"3.37.3"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T00:00:00Z","timestamp":1728604800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,1]]},"abstract":"Abstract<\/jats:title>Let \n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> be any positive integer. We prove that for every sufficiently large \n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> there exists a \n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-chromatic vertex-critical graph \n$G$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that \n$\\chi (G-R)=k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for every set \n$R \\subseteq E(G)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with \n$|R|\\le r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This partially solves a problem posed by Erd\u0151s in 1985, who asked whether the above statement holds for \n$k \\ge 4$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0963548324000324","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T07:06:24Z","timestamp":1728630384000},"page":"151-157","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Vertex-critical graphs far from edge-criticality"],"prefix":"10.1017","volume":"34","author":[{"given":"Anders","family":"Martinsson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4234-6136","authenticated-orcid":false,"given":"Raphael","family":"Steiner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"key":"S0963548324000324_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)90354-I"},{"key":"S0963548324000324_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00262-5"},{"key":"S0963548324000324_ref4","first-page":"111","volume-title":"Graph Theory in Memory of G. A. Dirac - Annals of Discrete Mathematics","author":"Erd\u0151s","year":"1985"},{"key":"S0963548324000324_ref2","doi-asserted-by":"publisher","DOI":"10.1201\/9781439863879"},{"key":"S0963548324000324_ref3","unstructured":"[3] Chung, F. (2012) Vertex-critical graphs with many extra edges. Online-database for Erd\u0151s\u2019 problems on graphs . Available at: https:\/\/mathweb.ucsd.edu\/~erdosproblems\/erdos\/newproblems\/NoncriticalEdges.html."},{"key":"S0963548324000324_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2023.109019"},{"key":"S0963548324000324_ref7","unstructured":"[7] Jensen, T. R. (1996) Structure of critical graphs. PhD thesis, Odense University, Denmark."},{"key":"S0963548324000324_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00394-1"},{"key":"S0963548324000324_ref11","doi-asserted-by":"publisher","DOI":"10.1090\/jams\/1028"},{"key":"S0963548324000324_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02026-1_22"},{"key":"S0963548324000324_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20224"},{"volume-title":"Wiley-Interscience Series in Discrete Mathematics and Optimization","year":"1995","author":"Jensen","key":"S0963548324000324_ref8"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000324","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T09:51:31Z","timestamp":1740390691000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000324\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,11]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["S0963548324000324"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000324","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2024,10,11]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}