{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T14:52:38Z","timestamp":1648997558966},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2016,3,31]],"date-time":"2016-03-31T00:00:00Z","timestamp":1459382400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2016,7]]},"abstract":"<jats:p>If <jats:italic>n<\/jats:italic> \u2a7e <jats:italic>k<\/jats:italic> + 1 and <jats:italic>G<\/jats:italic> is a connected <jats:italic>n<\/jats:italic>-vertex graph, then one can add <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548316000146_inline1\" \/><jats:tex-math>$\\binom{k}{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> edges to <jats:italic>G<\/jats:italic> so that the resulting graph contains the complete graph <jats:italic>K<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic>+1<\/jats:sub>. This yields that for any connected graph <jats:italic>G<\/jats:italic> with at least <jats:italic>k<\/jats:italic> + 1 vertices, one can add <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548316000146_inline1\" \/><jats:tex-math>$\\binom{k}{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> edges to <jats:italic>G<\/jats:italic> so that the resulting graph has chromatic number &gt; <jats:italic>k<\/jats:italic>. A long time ago, Bollob\u00e1s suggested that for every <jats:italic>k<\/jats:italic> \u2a7e 3 there exists a <jats:italic>k<\/jats:italic>-chromatic graph <jats:italic>G<jats:sub>k<\/jats:sub><\/jats:italic> such that after adding to it any <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548316000146_inline1\" \/><jats:tex-math>$\\binom{k}{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> \u2212 1 edges, the chromatic number of the resulting graph is still <jats:italic>k<\/jats:italic>. In this note we prove this conjecture.<\/jats:p>","DOI":"10.1017\/s0963548316000146","type":"journal-article","created":{"date-parts":[[2016,3,31]],"date-time":"2016-03-31T02:18:03Z","timestamp":1459390683000},"page":"592-594","source":"Crossref","is-referenced-by-count":0,"title":["Adding Edges to Increase the Chromatic Number of a Graph"],"prefix":"10.1017","volume":"25","author":[{"given":"ALEXANDR","family":"KOSTOCHKA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JAROSLAV","family":"NE\u0160ET\u0158IL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,3,31]]},"reference":[{"key":"S0963548316000146_ref2","first-page":"532","article-title":"Solution to advanced problem No 4526","volume":"61","author":"Descartes","year":"1954","journal-title":"Amer. Math. Monthly"},{"key":"S0963548316000146_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399004022"},{"key":"S0963548316000146_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39286-3_15"},{"key":"S0963548316000146_ref1","unstructured":"Bollob\u00e1s B. personal communication."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548316000146","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T22:16:23Z","timestamp":1555625783000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548316000146\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,31]]},"references-count":4,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["S0963548316000146"],"URL":"https:\/\/doi.org\/10.1017\/s0963548316000146","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,31]]}}}