{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T09:26:15Z","timestamp":1648805175011},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:00:00Z","timestamp":1496188800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2018,8]]},"DOI":"10.1007\/s00493-016-3556-x","type":"journal-article","created":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:11:21Z","timestamp":1496189481000},"page":"861-885","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["How Many Circuits Determine an Oriented Matroid?"],"prefix":"10.1007","volume":"38","author":[{"given":"Kolja","family":"Knauer","sequence":"first","affiliation":[]},{"given":"Luis Pedro","family":"Montejano","sequence":"additional","affiliation":[]},{"given":"Jorge Luis Ram\u00edrez","family":"Alfons\u00edn","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,31]]},"reference":[{"key":"3556_CR1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/978-94-009-0517-7_2","volume-title":"Cycles and Rays","author":"B. Alspach","year":"1990","unstructured":"B. Alspach, J.-C. Bermond and D. Sotteau: Decomposition into cycles I: Hamilton decompositions, in: Cycles and Rays, Springer, 1990, 9\u201318."},{"key":"3556_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1006\/jctb.2000.1996","volume":"81","author":"B. Alspach","year":"2001","unstructured":"B. Alspach and H. Gavlas: Cycle decomposition of Kn and Kn\u2013I, J. Combin. Th. Ser. B.\n                           81 (2001), 77\u201399.","journal-title":"J. Combin. Th. Ser. B."},{"key":"3556_CR3","first-page":"807","volume":"48","author":"L. Anderson","year":"2012","unstructured":"L. Anderson and E. Delucchi: Foundations for a theory of complex matroids, Disc. Comput. Geom.\n                           48 (2012), 807\u2013846.","journal-title":"Disc. Comput. Geom."},{"key":"3556_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511586507","volume-title":"Oriented matroids","author":"A. Bj\u00f6rner","year":"1999","unstructured":"A. Bj\u00f6rner, M. Las Vergnas, B. Sturmfels, N. White and G. M. Ziegler: Oriented matroids, vol. 46 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, second ed., 1999."},{"key":"3556_CR5","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/0095-8956(78)90080-1","volume":"24","author":"R. G. Bland","year":"1978","unstructured":"R. G. Bland and M. Las Vergnas: Orientability of matroids, J. Combinatorial Theory Ser. B.\n                           24 (1978), 94\u2013123.","journal-title":"J. Combinatorial Theory Ser. B."},{"key":"3556_CR6","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/BF00181184","volume":"63","author":"J. Bokowski","year":"1996","unstructured":"J. Bokowski, A. Guedes de Oliviera, U. Thiemann and A. Veloso da Costa: On the cube problem of Las Vergnas, Geom. Dedicata\n                           63 (1996), 25\u201343.","journal-title":"Geom. Dedicata"},{"key":"3556_CR7","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1006\/eujc.2000.0483","volume":"22","author":"J. Bokowski","year":"2001","unstructured":"J. Bokowski and H. Rohlfs: On a mutation problem for oriented matroids, European J. Combin.\n                           22 (2001), 617\u2013626. Combinatorial geometries (Luminy, 1999).","journal-title":"European J. Combin."},{"key":"3556_CR8","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1002\/jcd.21425","volume":"23","author":"J. Chappelon","year":"2015","unstructured":"J. Chappelon, K. Knauer, L. P. Montejano and J. L. Ram\u00edrez Alfons\u00edn: Conncted covering numbers, J. Comb. Design\n                           23 (2015), 534\u2013549.","journal-title":"J. Comb. Design"},{"key":"3556_CR9","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0012-365X(90)90333-D","volume":"79","author":"R. Cordovil","year":"1990","unstructured":"R. Cordovil and P. Duchet: On sign-invariance graphs of uniform oriented matroids, Discrete Math.\n                           79 (1990), 251\u2013257.","journal-title":"Discrete Math."},{"key":"3556_CR10","first-page":"355","volume-title":"Graph Theory in Paris","author":"I. P. Silva da","year":"2007","unstructured":"I. P. da Silva: Reconstruction of a rank 3 oriented matroid from its rank 2 signed circuits, in: Graph Theory in Paris, 2007, 355\u2013364."},{"key":"3556_CR11","doi-asserted-by":"publisher","first-page":"3574","DOI":"10.1016\/j.disc.2007.07.043","volume":"308","author":"I. P. F. Silva da","year":"2008","unstructured":"I. P. F. da Silva: Cubes and orientability, Discrete Math.\n                           308 (2008), 3574\u20133585.","journal-title":"Discrete Math."},{"key":"3556_CR12","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/0001-8708(91)90036-7","volume":"86","author":"A. Dress","year":"1991","unstructured":"A. Dress and W. Wenzel: Grassmann pl\u00fccker relations and matroids with coecients, Advanced in Mathematics\n                           86 (1991), 68\u2013110.","journal-title":"Advanced in Mathematics"},{"key":"3556_CR13","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1006\/jctb.2001.2063","volume":"84","author":"G. Fan","year":"2002","unstructured":"G. Fan: Subgraph coverings and edge switchings, J. Combin. Theory Ser. B\n                           84 (2002), 54\u201383.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3556_CR14","doi-asserted-by":"publisher","first-page":"1074","DOI":"10.1016\/j.jctb.2007.02.007","volume":"97","author":"J. Fink","year":"2007","unstructured":"J. Fink: Perfect matchings extend to Hamilton cycles in hypercubes, J. Combin. Theory, Ser. B\n                           97 (2007), 1074\u20131076.","journal-title":"J. Combin. Theory, Ser. B"},{"key":"3556_CR15","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0095-8956(78)90039-4","volume":"25","author":"J. Folkman","year":"1978","unstructured":"J. Folkman and J. Lawrence: Oriented matroids, J. Combin. Theory Ser. B\n                           25 (1978), 199\u2013236.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3556_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0012-365X(97)00246-X","volume":"187","author":"D. Forge","year":"1998","unstructured":"D. Forge and J. L. Ram\u00edrez Alfons\u00edn: Connected coverings and an application to oriented matroids, Discrete Math.\n                           187 (1998), 109\u2013121.","journal-title":"Discrete Math."},{"key":"3556_CR17","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/S0012-365X(02)00536-8","volume":"258","author":"D. Forge","year":"2002","unstructured":"D. Forge, J. L. Ram\u00edrez Alfons\u00edn and H. Yeun: Disconnected coverings for oriented matroids via simultaneous mutations, Discrete Math.\n                           258 (2002), 353\u2013359.","journal-title":"Discrete Math."},{"key":"3556_CR18","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1109\/TCS.1976.1084138","volume":"CAS-23","author":"M. R. Garey","year":"1976","unstructured":"M. R. Garey, D. S. Johnson and H. C. So: An application of graph coloring to printed circuit testing, IEEE Trans. Circuits and Systems, CAS-23 (1976), 591\u2013599.","journal-title":"IEEE Trans. Circuits and Systems"},{"key":"3556_CR19","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1006\/aima.1995.1036","volume":"113","author":"I. Gelfand","year":"1995","unstructured":"I. Gelfand, G. Rybnikov and D. Stone: Projective orientations of matroids, Advanced in Mathematics\n                           113 (1995), 118\u2013150.","journal-title":"Advanced in Mathematics"},{"key":"3556_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory","author":"C. Godsil","year":"2001","unstructured":"C. Godsil and G. Royle: Algebraic graph theory, New York, NY: Springer, 2001."},{"key":"3556_CR21","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1137\/0204019","volume":"4","author":"F. Hadlock","year":"1975","unstructured":"F. Hadlock: Finding a maximum cut of a planar graph in polynomial time, SIAM J. Comput.\n                           4 (1975), 221\u2013225.","journal-title":"SIAM J. Comput."},{"key":"3556_CR22","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0095-8956(86)90083-3","volume":"40","author":"Y. O. Hamidoune","year":"1986","unstructured":"Y. O. Hamidoune and M. Las Vergnas: Directed switching games on graphs and matroids, J. Combin. Theory Ser. B\n                           40 (1986), 237\u2013269.","journal-title":"J. Combin. Theory Ser. B"},{"key":"3556_CR23","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/S0012-365X(03)00058-X","volume":"269","author":"H.-J. Lai","year":"2003","unstructured":"H.-J. Lai and X. Li: Small cycle cover of 2-connected cubic graphs, Discrete Math.\n                           269 (2003), 295\u2013302.","journal-title":"Discrete Math."},{"key":"3556_CR24","first-page":"12","volume-title":"Regular polytopes and oriented matroids","author":"M. Las Vergnas","year":"1989","unstructured":"M. Las Vergnas, J.-P. Roudneff and I. Sal\u00e4un: Regular polytopes and oriented matroids, (1989), 12, preprint."},{"key":"3556_CR25","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1137\/0112059","volume":"12","author":"A. Lehman","year":"1964","unstructured":"A. Lehman: A solution of the Shannon switching game, J. Soc. Indust. Appl. Math.\n                           12 (1964), 687\u2013725.","journal-title":"J. Soc. Indust. Appl. Math."},{"key":"3556_CR26","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.jctb.2005.07.001","volume":"96","author":"M. Lemos","year":"2006","unstructured":"M. Lemos and J. Oxley: Matroid packing and covering with circuits through an element, J. Combin. Theory, Ser. B\n                           96 (2006), 135\u2013158.","journal-title":"J. Combin. Theory, Ser. B"},{"key":"3556_CR27","first-page":"256","volume":"78","author":"F. Levi","year":"1926","unstructured":"F. Levi: Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade, Ber. Math.-Phy. KI. Sachs. Akad. Wiss. Leipzig\n                           78 (1926), 256\u2013267.","journal-title":"Ber. Math.-Phy. KI. Sachs. Akad. Wiss. Leipzig"},{"key":"3556_CR28","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1137\/0122040","volume":"22","author":"D. W. Matula","year":"1972","unstructured":"D. W. Matula: k-components, clusters and slicings in graphs, SIAM J. Appl. Math.\n                           22 (1972), 459\u2013480.","journal-title":"SIAM J. Appl. Math."},{"key":"3556_CR29","doi-asserted-by":"publisher","first-page":"1335","DOI":"10.1016\/j.ejc.2009.11.009","volume":"31","author":"S. McGuinness","year":"2010","unstructured":"S. McGuinness: Circuit and fractional circuit covers of matroids, European Journal of Combinatorics\n                           31 (2010), 1335\u20131341.","journal-title":"European Journal of Combinatorics"},{"key":"3556_CR30","volume-title":"Matroid Theory","author":"J. Oxley","year":"2006","unstructured":"J. Oxley: Matroid Theory, vol. 3 of Oxford Graduate Texts in Mathematics, Oxford University Press, Oxford, second ed., 2006."},{"key":"3556_CR31","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/S0195-6698(88)80001-5","volume":"9","author":"J.-P. Roudneff","year":"1988","unstructured":"J.-P. Roudneff: Reconstruction of the orientation class of an oriented matroid, European J. Combin.\n                           9 (1988), 423\u2013429.","journal-title":"European J. Combin."},{"key":"3556_CR32","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/BF00151346","volume":"27","author":"J.-P. Roudneff","year":"1988","unstructured":"J.-P. Roudneff and B. Sturmfels: Simplicial cells in arrangements and mutuations of oriented matroids, Geometriae Dedicata\n                           27 (1988), 153\u2013170.","journal-title":"Geometriae Dedicata"},{"key":"3556_CR33","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0095-8956(80)90067-2","volume":"28","author":"P. Seymour","year":"1980","unstructured":"P. Seymour: Packing and covering with matroid circuits, J. Combin. Theory, Ser. B\n                           28 (1980), 237\u2013242.","journal-title":"J. Combin. Theory, Ser. B"},{"key":"3556_CR34","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/BF00181486","volume":"8","author":"R. W. Shannon","year":"1979","unstructured":"R. W. Shannon: Simplicial cells in arrangements of hyperplanes, Geometriae Dedicata\n                           8 (1979), 179\u2013187.","journal-title":"Geometriae Dedicata"},{"key":"3556_CR35","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.disc.2010.10.013","volume":"311","author":"F. Yang","year":"2011","unstructured":"F. Yang and X. Li: Small cycle covers of 3-connected cubic graphs, Discrete Math.\n                           311 (2011), 186\u2013196.","journal-title":"Discrete Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-016-3556-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-016-3556-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-016-3556-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T03:41:47Z","timestamp":1540352507000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-016-3556-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,31]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,8]]}},"alternative-id":["3556"],"URL":"https:\/\/doi.org\/10.1007\/s00493-016-3556-x","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,31]]}}}