{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T18:54:08Z","timestamp":1780599248483,"version":"3.54.1"},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5764,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:p>We prove that every connected graph of order <jats:italic>n<\/jats:italic> \u2265 2 has an induced subgraph with all degrees odd of order at least <jats:italic>cn<\/jats:italic>\/log <jats:italic>n<\/jats:italic>, where <jats:italic>c<\/jats:italic><jats:italic>is<\/jats:italic> a constant. We also give a bound in terms of chromatic number, and resolve the analogous problem for random graphs.<\/jats:p>","DOI":"10.1017\/s0963548300000389","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:18:24Z","timestamp":1221218304000},"page":"335-349","source":"Crossref","is-referenced-by-count":16,"title":["Large Induced Subgraphs with All Degrees Odd"],"prefix":"10.1017","volume":"1","author":[{"given":"A. D.","family":"Scott","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000389_ref005","unstructured":"[5] Radcliffe A. J. and Scott A. D. (submitted) Every tree has a large induced subgraph with all degrees odd."},{"key":"S0963548300000389_ref003","unstructured":"[3] Caro Y. , Krasikov I. and Roditty Y. (to appear) On induced subgraphs of trees with restricted degrees. Discrete Mathematics."},{"key":"S0963548300000389_ref002","unstructured":"[2] Caro Y. (to appear) On induced subgraphs with odd degrees."},{"key":"S0963548300000389_ref001","first-page":"180","volume-title":"Graph Theory, An Introductory Course","author":"Bollob\u00e1s","year":"1979"},{"key":"S0963548300000389_ref004","first-page":"551","volume-title":"Combinatorial Problems and Exercises","author":"Lov\u00e1sz","year":"1979"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300000389","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T20:07:31Z","timestamp":1558037251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300000389\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,12]]}},"alternative-id":["S0963548300000389"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300000389","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,12]]}}}