{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:50:59Z","timestamp":1780386659059,"version":"3.54.1"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2008,3,1]],"date-time":"2008-03-01T00:00:00Z","timestamp":1204329600000},"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":[[2008,3]]},"abstract":"<jats:p>A proper vertex colouring of a graph is <jats:italic>equitable<\/jats:italic> if the sizes of colour classes differ by at most one. We present a new shorter proof of the celebrated Hajnal\u2013Szemer\u00e9di theorem: for every positive integer <jats:italic>r<\/jats:italic>, every graph with maximum degree at most <jats:italic>r<\/jats:italic> has an equitable colouring with <jats:italic>r<\/jats:italic>+1 colours. The proof yields a polynomial time algorithm for such colourings.<\/jats:p>","DOI":"10.1017\/s0963548307008619","type":"journal-article","created":{"date-parts":[[2007,7,5]],"date-time":"2007-07-05T08:22:11Z","timestamp":1183623731000},"page":"265-270","source":"Crossref","is-referenced-by-count":71,"title":["A Short Proof of the Hajnal\u2013Szemer\u00e9di Theorem on Equitable Colouring"],"prefix":"10.1017","volume":"17","author":[{"given":"H. A.","family":"KIERSTEAD","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. V.","family":"KOSTOCHKA","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,3,1]]},"reference":[{"key":"S0963548307008619_ref13","doi-asserted-by":"crossref","unstructured":"[13] Pemmaraju S. V. (2001) Equitable colorings extend Chernoff\u2013Hoeffding bounds. In Proc. 5th International Workshop on Randomization and Approximation Techniques in Computer Science (APPROX-RANDOM 2001), pp. 285\u2013296.","DOI":"10.1007\/3-540-44666-4_31"},{"key":"S0963548307008619_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04363-9"},{"key":"S0963548307008619_ref11","unstructured":"[11] Mydlarz M. and Szemer\u00e9di E. Algorithmic Brooks' theorem. Manuscript."},{"key":"S0963548307008619_ref9","first-page":"55","article-title":"Extremal problems on packing of graphs","volume":"1","author":"Kostochka","year":"2006","journal-title":"Oberwolfach Reports"},{"key":"S0963548307008619_ref12","doi-asserted-by":"publisher","DOI":"10.2307\/2308928"},{"key":"S0963548307008619_ref5","first-page":"601","volume-title":"Combinatorial Theory and its Application","author":"Hajnal","year":"1970"},{"key":"S0963548307008619_ref16","doi-asserted-by":"publisher","DOI":"10.1137\/1015072"},{"key":"S0963548307008619_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01626028"},{"key":"S0963548307008619_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10137"},{"key":"S0963548307008619_ref4","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0039"},{"key":"S0963548307008619_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306007899"},{"key":"S0963548307008619_ref2","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1994.1047"},{"key":"S0963548307008619_ref14","first-page":"201","volume-title":"Combinatorics: Proc. British Combinatorial Conference 1973","author":"Seymour","year":"1974"},{"key":"S0963548307008619_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10031"},{"key":"S0963548307008619_ref15","volume-title":"Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations","author":"Smith","year":"1996"},{"key":"S0963548307008619_ref3","first-page":"159","volume-title":"Theory of Graphs and its Applications","author":"Erd\u0151s","year":"1964"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548307008619","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,7]],"date-time":"2019-04-07T20:29:04Z","timestamp":1554668944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548307008619\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,3]]}},"alternative-id":["S0963548307008619"],"URL":"https:\/\/doi.org\/10.1017\/s0963548307008619","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}