{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:46:28Z","timestamp":1740109588535,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T00:00:00Z","timestamp":1668816000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T00:00:00Z","timestamp":1668816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T030461\/1"],"award-info":[{"award-number":["EP\/T030461\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001695","name":"Japan Science and Technology Corporation","doi-asserted-by":"publisher","award":["JPMJER1903"],"award-info":[{"award-number":["JPMJER1903"]}],"id":[{"id":"10.13039\/501100001695","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18K11155"],"award-info":[{"award-number":["18K11155"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2023,1]]},"DOI":"10.1007\/s00454-022-00459-9","type":"journal-article","created":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T21:17:00Z","timestamp":1668892620000},"page":"192-208","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Vertex Splitting, Coincident Realisations, and Global Rigidity of Braced Triangulations"],"prefix":"10.1007","volume":"69","author":[{"given":"James","family":"Cruickshank","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1381-8675","authenticated-orcid":false,"given":"Bill","family":"Jackson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin-ichi","family":"Tanigawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,19]]},"reference":[{"key":"459_CR1","unstructured":"Abbott, T.: Generalizations of Kempe\u2019s Universality Theorem. MSc thesis, Massachusetts Institute of Technology (2008)"},{"issue":"2","key":"459_CR2","doi-asserted-by":"publisher","first-page":"145","DOI":"10.26493\/1855-3974.459.c4d","volume":"9","author":"G Brinkmann","year":"2015","unstructured":"Brinkmann, G., Larson, C., Souffriau, J., Van Cleemput, N.: Construction of planar $$4$$-connected triangulations. Ars Math. Contemp. 9(2), 145\u2013149 (2015)","journal-title":"Ars Math. Contemp."},{"issue":"4","key":"459_CR3","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/s00454-004-1124-4","volume":"33","author":"R Connelly","year":"2005","unstructured":"Connelly, R.: Generic global rigidity. Discrete Comput. Geom. 33(4), 549\u2013563 (2005)","journal-title":"Discrete Comput. Geom."},{"key":"459_CR4","unstructured":"Connelly, R.: Questions, conjectures and remarks on globally rigid tensegrities (2009). http:\/\/www.math.cornell.edu\/~connelly\/09-Thoughts.pdf"},{"key":"459_CR5","doi-asserted-by":"crossref","unstructured":"Connelly, R., Whiteley, W.J.: Global rigidity: the effect of coning. Discrete Comput. Geom. 43(4), 717\u2013735 (2010)","DOI":"10.1007\/s00454-009-9220-0"},{"key":"459_CR6","unstructured":"Cruickshank, J., Jackson, B., Tanigawa, S.: Global rigidity of triangulated manifolds (2022). arXiv:2204.02503"},{"issue":"3","key":"459_CR7","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/s00373-013-1390-0","volume":"31","author":"ZS Fekete","year":"2015","unstructured":"Fekete, Z.S., Jord\u00e1n, T., Kaszanitzky, V.E.: Rigid two-dimensional frameworks with two coincident points. Graphs Combin. 31(3), 585\u2013599 (2015)","journal-title":"Graphs Combin."},{"key":"459_CR8","doi-asserted-by":"crossref","unstructured":"Gluck, H.: Almost all simply connected closed surfaces are rigid. In: Geometric Topology (Park City 1974). Lecture Notes in Math., vol. 438, pp. 225\u2013239. Springer, Berlin (1975)","DOI":"10.1007\/BFb0066118"},{"key":"459_CR9","doi-asserted-by":"crossref","unstructured":"Gortler, S.J., Healy, A.D., Thurston, D.P.: Characterizing generic global rigidity. Am. J. Math. 132(4), 897\u2013939 (2010)","DOI":"10.1353\/ajm.0.0132"},{"key":"459_CR10","doi-asserted-by":"crossref","unstructured":"Guler, H., Jackson, B.: Coincident rigidity of $$2$$-dimensional frameworks. Graphs Combin. 38(4), #\u00a0128 (2022)","DOI":"10.1007\/s00373-022-02540-9"},{"key":"459_CR11","doi-asserted-by":"crossref","unstructured":"Hendrickson, B.: Conditions for unique graph realizations. SIAM J. Comput. 21(1), 65\u201384 (1992)","DOI":"10.1137\/0221008"},{"key":"459_CR12","doi-asserted-by":"crossref","unstructured":"Jackson, B., Jord\u00e1n, T.: Connected rigidity matroids and unique realizations of graphs. J. Combin. Theory Ser. B 94(1), 1\u201329 (2005)","DOI":"10.1016\/j.jctb.2004.11.002"},{"key":"459_CR13","doi-asserted-by":"crossref","unstructured":"Jackson, B., Kaszanitzky, V.E., Nixon, A.: Rigid cylindrical frameworks with two coincident points. Graphs Combin. 35(1), 141\u2013168 (2019)","DOI":"10.1007\/s00373-018-1983-8"},{"key":"459_CR14","doi-asserted-by":"crossref","unstructured":"Jackson, B., Nixon, A.: Global rigidity of generic frameworks on the cylinder. J. Combin. Theory Ser. B 139, 193\u2013229 (2019)","DOI":"10.1016\/j.jctb.2019.03.002"},{"key":"459_CR15","doi-asserted-by":"crossref","unstructured":"Jord\u00e1n, T., Kir\u00e1ly, C., Tanigawa, S.: Generic global rigidity of body-hinge frameworks. J. Combin. Theory Ser. B 117, 59\u201376 (2016)","DOI":"10.1016\/j.jctb.2015.11.003"},{"key":"459_CR16","unstructured":"Jord\u00e1n, T., Kir\u00e1ly, C., Tanigawa, S.: On the vertex splitting operation in globally rigid body-hinge graphs. Technical report TR-2019-16, Egerv\u00e1ry Research Group (2019). https:\/\/egres.elte.hu\/tr\/egres-19-16.pdf"},{"key":"459_CR17","doi-asserted-by":"crossref","unstructured":"Jord\u00e1n, T., Tanigawa, S.: Global rigidity of triangulations with braces. J. Combin. Theory Ser. B 136, 249\u2013288 (2019)","DOI":"10.1016\/j.jctb.2018.11.003"},{"key":"459_CR18","unstructured":"Jord\u00e1n, T., Whiteley, W.: Global rigidity. In: Handbook of Discrete and Computational Geometry, 3rd ed. Discrete Mathematics and its Applications, pp. 1661\u20131694. CRC Press, Boca Raton (2017)"},{"key":"459_CR19","doi-asserted-by":"crossref","unstructured":"Laman, G.: On graphs and rigidity of plane skeletal structures. J. Eng. Math. 4(4), 331\u2013340 (1970)","DOI":"10.1007\/BF01534980"},{"issue":"2","key":"459_CR20","first-page":"145","volume":"50","author":"A Nakamoto","year":"2002","unstructured":"Nakamoto, A., Hama, M.: Generating $$4$$-connected triangulations on closed surfaces. Mem. Osaka Kyoiku Univ. Ser. III Nat. Sci. Appl. Sci. 50(2), 145\u2013153 (2002)","journal-title":"Mem. Osaka Kyoiku Univ. Ser. III Nat. Sci. Appl. Sci."},{"issue":"1","key":"459_CR21","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1002\/zamm.19270070107","volume":"7","author":"H Pollaczek-Geiringer","year":"1927","unstructured":"Pollaczek-Geiringer, H.: \u00dcber die Gliederung ebener Fachwerke. Z. Angew. Math. Mech. 7(1), 58\u201372 (1927)","journal-title":"Z. Angew. Math. Mech."},{"key":"459_CR22","unstructured":"Saxe, J.B.: Embeddability of weighted graphs in $$k$$-space is strongly NP-hard. Technical report, Computer Science Department, Carnegie-Mellon University, Pittsburgh (1979)"},{"key":"459_CR23","unstructured":"Schulze, B., Whiteley, W.: Rigidity and scene analysis. In: Handbook of Discrete and Computational Geometry, 3rd ed., pp. 1593\u20131632. CRC Press, Boca Raton (2017)"},{"issue":"1","key":"459_CR24","first-page":"115","volume":"306","author":"W Whiteley","year":"1988","unstructured":"Whiteley, W.: Infinitesimally rigid polyhedra. II. Modified spherical frameworks. Trans. Am. Math. Soc. 306(1), 115\u2013139 (1988)","journal-title":"Trans. Am. Math. Soc."},{"key":"459_CR25","first-page":"23","volume":"16","author":"W Whiteley","year":"1990","unstructured":"Whiteley, W.: Vertex splitting in isostatic frameworks. Struct. Topol. 16, 23\u201330 (1990)","journal-title":"Struct. Topol."},{"key":"459_CR26","doi-asserted-by":"crossref","unstructured":"Whiteley, W.: Some matroids from discrete applied geometry. In: Matroid Theory (Seattle 1995). Contemp. Math., vol. 197, pp. 171\u2013311. American Mathematical Society, Providence (1996)","DOI":"10.1090\/conm\/197\/02540"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-022-00459-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-022-00459-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-022-00459-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T20:04:14Z","timestamp":1672603454000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-022-00459-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,19]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["459"],"URL":"https:\/\/doi.org\/10.1007\/s00454-022-00459-9","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2022,11,19]]},"assertion":[{"value":"20 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 November 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}