{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T04:39:52Z","timestamp":1791088792596,"version":"4.1.0"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>An efficient algorithm listing all minimal vertex separators of an undirected graph is given. The algorithm needs polynomial time per separator that is found.<\/jats:p>","DOI":"10.1137\/s009753979427087x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"605-613","source":"Crossref","is-referenced-by-count":61,"title":["Listing all Minimal Separators of a Graph"],"prefix":"10.1137","volume":"27","author":[{"given":"T.","family":"Kloks","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Kratsch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934985"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(91)90006-K"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(89)90031-0"},{"key":"R4","first-page":"1","volume":"11","author":"Bodlaender H.","year":"1993","journal-title":"Acta Cybernet."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"H. Bodlaender,\n                      A linear time algorithm for finding tree\u2010decompositions of small treewidth\n                      , Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 226\u2013234.","DOI":"10.1145\/167088.167161"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S089548019223992X"},{"key":"R7","unstructured":"H. Bodlaender, T. Kloks, D. Kratsch, and H. M\u00fcller,\n                      Treewidth and minimum fill\u2010in on d\u2010trapezoid graphs\n                      , Technical Report UU\u2010CS\u20101995\u201034, Utrecht University, The Netherlands, 1995."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90030-9"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569913"},{"key":"R10","volume-title":"Algorithmic graph theory and perfect graphs","author":"Golumbic Martin","year":"1980"},{"key":"R11","unstructured":"A. Kanevsky,\n                      On the number of minimum size separating vertex sets in a graph and how to find all of them\n                      , Proceedings of the First Annual ACM\u2010SIAM Symposium on Discrete Algorithms, 1990, pp. 411\u2013421."},{"key":"R12","doi-asserted-by":"crossref","unstructured":"T. Kloks,\n                      Treewidth\u2014Computations and Approximations\n                      , Springer\u2010Verlag, Lecture Notes in Computer Science 842, 1994.","DOI":"10.1007\/BFb0045375"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"T. Kloks, Treewidth of circle graphs, Lecture Notes in Comput. Sci., Vol. 762, Springer, Berlin, 1993, 108\u201311795e:05114","DOI":"10.1007\/3-540-57568-5_240"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"T. Kloks,\n                      Minimum fill\u2010in for chordal bipatite graphs\n                      , Technical Report RUU\u2010CS\u201093\u201011, Department of Computer Science, Utrecht University, The Netherlands, 1993.","DOI":"10.1007\/3-540-56503-5_11"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1995.1037"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00206-X"},{"key":"R17","unstructured":"D. Kratsch,\n                      The structure of graphs and the design of efficient algorithms\n                      , Habilitation (thesis), F.\u2010Schiller\u2010Universit\u00e4t Jena, 1996."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"A. Parra and P. Scheffler,\n                      How to use the minimal separators of a graph for its chordal triangulation\n                      , Proceedings of the 22rd International Colloquium on Automata, Languages and Programming, Springer\u2010Verlag, Lecture Notes in Computer Science 944, 1995, pp. 123\u2013134.","DOI":"10.1007\/3-540-60084-1_68"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(85)90051-2"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(81)90072-7"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S009753979427087X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:13:31Z","timestamp":1787336011000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S009753979427087X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S009753979427087X"],"URL":"https:\/\/doi.org\/10.1137\/s009753979427087x","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}