{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T13:08:44Z","timestamp":1783170524900,"version":"3.54.6"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2011,6,20]],"date-time":"2011-06-20T00:00:00Z","timestamp":1308528000000},"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":[[2011,9]]},"abstract":"<jats:p>An old result by Shearer relates the Lov\u00e1sz local lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard-core lattice gas on graphs. We use this connection and a recent result on the analyticity of the logarithm of the partition function of the abstract polymer gas to get an improved version of the Lov\u00e1sz local lemma. As an application we obtain tighter bounds on conditions for the existence of Latin transversal matrices.<\/jats:p>","DOI":"10.1017\/s0963548311000253","type":"journal-article","created":{"date-parts":[[2011,6,20]],"date-time":"2011-06-20T04:29:49Z","timestamp":1308544189000},"page":"709-719","source":"Crossref","is-referenced-by-count":47,"title":["An Improvement of the Lov\u00e1sz Local Lemma via Cluster Expansion"],"prefix":"10.1017","volume":"20","author":[{"given":"RODRIGO","family":"BISSACOT","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ROBERTO","family":"FERN\u00c1NDEZ","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ALDO","family":"PROCACCI","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"BENEDETTO","family":"SCOPPOLA","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2011,6,20]]},"reference":[{"key":"S0963548311000253_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-007-0279-2"},{"key":"S0963548311000253_ref2","unstructured":"[2] B\u00f6ttcher J. , Kohayakawa Y. and Procacci A. Properly coloured copies and rainbow copies of large graphs with small maximum degree. Random Struct. Alg., to appear. Preprint. arXiv.org\/abs\/1007.3767"},{"key":"S0963548311000253_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007182"},{"key":"S0963548311000253_ref10","doi-asserted-by":"publisher","DOI":"10.1145\/1667053.1667060"},{"key":"S0963548311000253_ref12","unstructured":"[12] Pegden W. An extension of the Moser-Tardos algorithmic local lemma. Preprint. arXiv.org\/abs\/1102.2853"},{"key":"S0963548311000253_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301004758"},{"key":"S0963548311000253_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470277331"},{"key":"S0963548311000253_ref5","first-page":"609","volume-title":"Infinite and Finite Sets II","author":"Erd\u0151s","year":"1975"},{"key":"S0963548311000253_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-004-2055-4"},{"key":"S0963548311000253_ref9","volume-title":"Probabilistic Methods for Algorithmic Discrete Mathematics","author":"Molloy","year":"1998"},{"key":"S0963548311000253_ref13","volume-title":"Statistical Mechanics: Rigorous Results","author":"Ruelle","year":"1969"},{"key":"S0963548311000253_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90040-4"},{"key":"S0963548311000253_ref11","unstructured":"[11] Ndreca S. , Procacci A. and Scoppola B. Improved bounds on coloring of graphs. Preprint. arXiv.org\/abs\/1005.1875"},{"key":"S0963548311000253_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579368"},{"key":"S0963548311000253_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095673"},{"key":"S0963548311000253_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90044-9"},{"key":"S0963548311000253_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000253","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T02:33:29Z","timestamp":1556332409000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000253\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,20]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["S0963548311000253"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000253","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,20]]}}}