{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:32Z","timestamp":1787321132715,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper presents new results on nonseparating cocircuits in binary matroids. The first result states that for any 3-connected binary matroid $M$ and for any basis $B$ of $M$, there exists at least two nonseparating $B$-fundamental cocircuits in $M$. The second result provides a weakened version of this result for nonseparable binary matroids that are also simple and cosimple. The final states that if $M$ is a nonseparable binary matroid, $D$ is a nonseparating cocircuit of $M$, and $e$ is an element of $D$, then $M$ is graphic if and only if $M\/e$ is graphic and has a realization $H$ in which $D-\\{e\\}$ is a subset of the star of some node of $H$. All of these results are shown to lead to efficient algorithms.<\/jats:p>","DOI":"10.1137\/21m139339x","type":"journal-article","created":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T10:44:25Z","timestamp":1640083465000},"page":"3030-3049","source":"Crossref","is-referenced-by-count":1,"title":["Nonseparating Cocircuits in Binary Matroids"],"prefix":"10.1137","volume":"35","author":[{"given":"Donald K.","family":"Wagner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,12,21]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(82)90214-2"},{"key":"atypb2","first-page":"91","author":"Bixby R. E.","year":"1979","journal-title":"New York"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1287\/moor.5.3.321"},{"key":"atypb4","first-page":"551","author":"Bixby R. E.","year":"1995","journal-title":"Amsterdam"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(87)90004-6"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1287\/moor.13.1.99"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-013-0208-3"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1980-057-7"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(82)90244-0"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(80)90042-2"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.07.001"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2014.12.003"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/0202012"},{"key":"atypb14","unstructured":"M. Iri,\n                      A necessary and sufficient condition for a matrix to be the loop or cut-set matrix of a graph and a practical method for the topological synthesis of networks\n                      , RAAG Research Notes, 3rd Ser., 50 (1962), pp. 1-40."},{"key":"atypb15","unstructured":"M. Iri,\n                      On the synthesis of the loop and cutset matrices and the related problems\n                      , RAAG Memoirs 4, A-XIII (1968), pp. 376-410."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190040103"},{"key":"atypb17","first-page":"345","volume":"1981","author":"Kelmans A. K.","journal-title":"Amsterdam"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2003.12.022"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.05.055"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2008.05.001"},{"key":"atypb21","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1002\/jgt.20446","volume":"64","author":"Lemos M.","year":"2009","journal-title":"J. Graph Theory"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.08.007"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s00026-015-0255-z"},{"key":"atypb24","doi-asserted-by":"crossref","DOI":"10.1109\/TCT.1959.1086609","volume":"6","author":"L\u00f6fgren L.","year":"1959","journal-title":"IRE Trans. Circuit Theory"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(59)90521-6"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1999.1949"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2008.01.007"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100054633"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2000.0407"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2007.05.001"},{"key":"atypb31","doi-asserted-by":"crossref","unstructured":"J. Oxley,\n                      Matroid Theory\n                      , Oxford University Press, Oxford, UK, 2011.","DOI":"10.1093\/acprof:oso\/9780198566946.001.0001"},{"key":"atypb32","unstructured":"R. Tamari,\n                      Combinatorial Algorithms in Certain Classes of Binary Matroids\n                      , Ph.D. thesis, Cornell University, Ithaca, New York, 1977."},{"key":"atypb33","first-page":"144","volume":"88","author":"Tutte W. T.","year":"1959","journal-title":"Trans. Amer. Math. Soc."},{"key":"atypb34","first-page":"905","volume":"11","author":"Tutte W. T.","year":"1960","journal-title":"Proc. Amer. Math. Soc."},{"key":"atypb35","first-page":"734","volume":"13","author":"Tutte W. T.","year":"1963","journal-title":"Proc. Lond. Math. Soc."},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1964-011-0"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.001"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.6028\/jres.071B.028"},{"key":"atypb39","doi-asserted-by":"crossref","unstructured":"W. T. Tutte,\n                      Connectivity in Graphs\n                      , University of Toronto Press, Toronto, 1966.","DOI":"10.3138\/9781487584863"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1966-129-2"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2010.01.005"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.2307\/2371127"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1999.1908"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M139339X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:07:28Z","timestamp":1787317648000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M139339X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/21M139339X"],"URL":"https:\/\/doi.org\/10.1137\/21m139339x","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}