{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:00:23Z","timestamp":1777366823615,"version":"3.51.4"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2012,11,6]],"date-time":"2012-11-06T00:00:00Z","timestamp":1352160000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2013,11]]},"DOI":"10.1007\/s00373-012-1244-1","type":"journal-article","created":{"date-parts":[[2012,11,5]],"date-time":"2012-11-05T03:54:55Z","timestamp":1352087695000},"page":"1675-1688","source":"Crossref","is-referenced-by-count":10,"title":["Irreducible Triangulations of Surfaces with Boundary"],"prefix":"10.1007","volume":"29","author":[{"given":"Alexandre","family":"Boulch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c9ric","family":"Colin de Verdi\u00e8re","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Atsuhiro","family":"Nakamoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,11,6]]},"reference":[{"issue":"3","key":"1244_CR1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1002\/jgt.3190100313","volume":"10","author":"D. Archdeacon","year":"1986","unstructured":"Archdeacon D.: The nonorientable genus is additive. J. Graph Theory 10(3), 363\u2013383 (1986)","journal-title":"J. Graph Theory"},{"key":"1244_CR2","doi-asserted-by":"crossref","unstructured":"Armstrong, M.A.: Basic topology. Undergraduate Texts in Mathematics. Springer, Berlin (1983)","DOI":"10.1007\/978-1-4757-1793-8"},{"key":"1244_CR3","doi-asserted-by":"crossref","unstructured":"Attali, D., Lieutier, A., Salinas, D.: Efficient data structure for representing and simplifying simplicial complexes in high dimensions. In: Proceedings of the 27th Annual Symposium on Computational Geometry (SOCG), ACM, pp. 501\u2013509 (2011)","DOI":"10.1145\/1998196.1998277"},{"key":"1244_CR4","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/0095-8956(82)90041-7","volume":"33","author":"D. Barnette","year":"1982","unstructured":"Barnette D.: Generating the triangulations of the projective plane. J. Comb. Theory Ser. B 33, 222\u2013230 (1982)","journal-title":"J. Comb. Theory Ser. B"},{"key":"1244_CR5","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/BF02767355","volume":"62","author":"D.W. Barnette","year":"1988","unstructured":"Barnette D.W., Edelson A.: All orientable 2\u2013manifolds have finitely many minimal triangulations. Isr. J. Math. 62, 90\u201398 (1988)","journal-title":"Isr. J. Math."},{"key":"1244_CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF02764905","volume":"67","author":"D.W. Barnette","year":"1989","unstructured":"Barnette D.W., Edelson A.: All 2-manifolds have finitely many minimal triangulations. Isr. J. Math. 67, 123\u2013128 (1989)","journal-title":"Isr. J. Math."},{"key":"1244_CR7","first-page":"258","volume":"247","author":"C. Berge","year":"1958","unstructured":"Berge C.: Sur le couplage maximum d\u2019un graphe. Comptes rendus hebdomadaires des S\u00e9ances de l\u2019Acad\u00e9mie des Sciences [Paris] 247, 258\u2013259 (1958)","journal-title":"Comptes rendus hebdomadaires des S\u00e9ances de l\u2019Acad\u00e9mie des Sciences [Paris]"},{"issue":"1\u20132","key":"1244_CR8","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.comgeo.2007.10.010","volume":"41","author":"E.W. Chambers","year":"2008","unstructured":"Chambers E.W., Colin de Verdi\u00e8re \u00c9., Erickson J., Lazarus F., Whittlesey K.: Splitting (complicated) surfaces is hard. Comput. Geom. Theory Appl. 41(1\u20132), 94\u2013110 (2008)","journal-title":"Comput. Geom. Theory Appl."},{"issue":"2","key":"1244_CR9","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.comgeo.2003.07.001","volume":"27","author":"S.-W. Cheng","year":"2004","unstructured":"Cheng S.-W., Dey T.K., Poon S.-H.: Hierarchy of surface models and irreducible triangulations. Comput. Geom. Theory Appl. 27(2), 135\u2013150 (2004)","journal-title":"Comput. Geom. Theory Appl."},{"key":"1244_CR10","unstructured":"Dey, T.K., Edelsbrunner, H., Guha, S., Nekhayev, D.V.: Topology preserving edge contraction. Publications de l\u2019Institut Math\u00e9matique (Beograd) (N.S.) 66(80), 23\u201345 (1999) [Geometric combinatorics (Kotor, 1998)]"},{"key":"1244_CR11","doi-asserted-by":"crossref","unstructured":"Fujisawa, J., Nakamoto, A., Ozeki, K.: Hamiltonian cycles in bipartite toroidal graphs with a partite set of degree four vertices. J. Comb. Theory Ser. B. http:\/\/dx.doi.org\/10.1016\/j.jctb.2012.08.004 (2012)","DOI":"10.1016\/j.jctb.2012.08.004"},{"key":"1244_CR12","unstructured":"Gao, Z., Richmond, L.B., Thomassen, C.: Irreducible triangulations and triangular embeddings on a surface. Technical Report CORR 91-07, University of Waterloo, Canada (1991)"},{"key":"1244_CR13","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1006\/jctb.1996.0064","volume":"68","author":"Z. Gao","year":"1996","unstructured":"Gao Z., Richter R.B., Seymour P.D.: Irreducible triangulations of surfaces. J. Comb. Theory Ser. B 68, 206\u2013217 (1996)","journal-title":"J. Comb. Theory Ser. B"},{"key":"1244_CR14","unstructured":"Henle, M.: A combinatorial introduction to topology. Dover Publications, USA (1994)"},{"key":"1244_CR15","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.jctb.2010.01.004","volume":"100","author":"G. Joret","year":"2010","unstructured":"Joret G., Wood D.R.: Irreducible triangulations are small. J. Comb. Theory Ser. B 100, 446\u2013455 (2010)","journal-title":"J. Comb. Theory Ser. B"},{"issue":"1","key":"1244_CR16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF02414187","volume":"145","author":"M. Jungerman","year":"1980","unstructured":"Jungerman M., Ringel G.: Minimal triangulations on orientable surfaces. Acta Math. 145(1), 121\u2013154 (1980)","journal-title":"Acta Math."},{"key":"1244_CR17","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1006\/jctb.1996.0053","volume":"68","author":"M. Juvan","year":"1996","unstructured":"Juvan M., Malnic\u0306 A., Mohar B.: Systems of curves on surfaces. J. Comb. Theory Ser. B 68, 7\u201322 (1996)","journal-title":"J. Comb. Theory Ser. B"},{"key":"1244_CR18","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1137\/070693540","volume":"23","author":"K. Kawarabayashi","year":"2008","unstructured":"Kawarabayashi K., Mukae R., Nakamoto A.: K 6-minors in triangulations on the Klein bottle. SIAM J. Discrete Math. 23, 96\u2013108 (2008)","journal-title":"SIAM J. Discrete Math."},{"key":"1244_CR19","first-page":"52","volume":"30","author":"S. Lawrencenko","year":"1987","unstructured":"Lawrencenko S.: The irreducible triangulations of the torus. Ukrain. Geom. Sb. 30, 52\u201362 (1987)","journal-title":"Ukrain. Geom. Sb."},{"issue":"1","key":"1244_CR20","first-page":"57","volume":"64","author":"A. Malnic\u0306","year":"1995","unstructured":"Malnic\u0306 A., Nedela R.: k-minimal triangulations of surfaces. Acta Mathematica Universitatis Comenianae 64(1), 57\u201376 (1995)","journal-title":"Acta Mathematica Universitatis Comenianae"},{"issue":"1","key":"1244_CR21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0095-8956(87)90028-1","volume":"43","author":"G.L. Miller","year":"1987","unstructured":"Miller G.L.: An additivity theorem for the genus of a graph. J. Comb. Theory Ser. B 43(1), 25\u201347 (1987)","journal-title":"J. Comb. Theory Ser. B"},{"key":"1244_CR22","unstructured":"Mohar, B., Thomassen, C.: Graphs on surfaces. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, USA (2001)"},{"key":"1244_CR23","unstructured":"Mukae, R., Nakamoto, A.: K 6-minors in triangulations on the nonorientable surface of genus 4 (in preparation)"},{"key":"1244_CR24","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1002\/jgt.20360","volume":"60","author":"R. Mukae","year":"2009","unstructured":"Mukae R., Nakamoto A.: K 6-minors in triangulations and complete quadrangulations. J. Graph Theory 60, 302\u2013312 (2009)","journal-title":"J. Graph Theory"},{"key":"1244_CR25","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s00373-010-0931-z","volume":"26","author":"R. Mukae","year":"2010","unstructured":"Mukae R., Nakamoto A., Oda Y., Suzuki Y.: K 6-minors in triangulations on the nonorientable surface of genus 3. Graphs Comb. 26, 559\u2013570 (2010)","journal-title":"Graphs Comb."},{"issue":"2","key":"1244_CR26","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1002\/jgt.3190200211","volume":"20","author":"A. Nakamoto","year":"1995","unstructured":"Nakamoto A., Ota K.: Note on irreducible triangulations of surfaces. J. Graph Theory 20(2), 227\u2013233 (1995)","journal-title":"J. Graph Theory"},{"key":"1244_CR27","first-page":"1","volume":"47","author":"S. Negami","year":"1999","unstructured":"Negami S.: Diagonal flips of triangulations on surfaces, a survey. Yokohama Math. J. 47, 1\u201340 (1999)","journal-title":"Yokohama Math. J."},{"issue":"1\u20133","key":"1244_CR28","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0012-365X(93)E0101-9","volume":"135","author":"S. Negami","year":"1994","unstructured":"Negami S.: Diagonal flips in triangulations of surfaces. Discrete Math. 135(1\u20133), 225\u2013232 (1994)","journal-title":"Discrete Math."},{"key":"1244_CR29","doi-asserted-by":"crossref","unstructured":"Schipper, H.: Generating triangulations of 2-manifolds. In: Computational Geometry\u2014Methods, Algorithms and Applications: Proceedings of International Workshop Computational Geomettry CG \u201991. Lecture Notes in Computer Science, Vol. 553, pp. 237\u2013248 (1991)","DOI":"10.1007\/3-540-54891-2_18"},{"key":"1244_CR30","unstructured":"Schrijver, A.: Combinatorial Optimization. Polyhedra and Efficiency. Algorithms and Combinatorics, Vol. 24. Springer, Berlin (2003)"},{"key":"1244_CR31","volume-title":"Vorlesungen \u00fcber die Theorie der Polyeder","author":"E. Steinitz","year":"1934","unstructured":"Steinitz E., Rademacher H.: Vorlesungen \u00fcber die Theorie der Polyeder. Springer, Berlin (1934)"},{"key":"1244_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4372-4","volume-title":"Classical topology and combinatorial group theory","author":"J. Stillwell","year":"1993","unstructured":"Stillwell J.: Classical topology and combinatorial group theory. Graduate Texts in Mathematics. Springer, Berlin (1993)"},{"key":"1244_CR33","unstructured":"Sulanke, T.: Generating irreducible triangulations of surfaces. arXiv:math\/0606687 (2006)"},{"key":"1244_CR34","unstructured":"Sulanke, T.: Irreducible triangulations of low genus surfaces. arXiv:math\/0606690 (2006)"},{"key":"1244_CR35","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1016\/j.jctb.2006.05.001","volume":"96","author":"T. Sulanke","year":"2006","unstructured":"Sulanke T.: Note on the irreducible triangulations of the Klein bottle. J. Comb. Theory, Ser. B 96, 964\u2013972 (2006)","journal-title":"J. Comb. Theory, Ser. B"},{"issue":"5","key":"1244_CR36","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.ejc.2011.01.009","volume":"32","author":"D.B. West","year":"2011","unstructured":"West D.B.: A short proof of the Berge\u2013Tutte formula and the Gallai\u2013Edmonds structure theorem. Eur. J. Comb. 32(5), 674\u2013676 (2011)","journal-title":"Eur. J. Comb."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-012-1244-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00373-012-1244-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-012-1244-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,5]],"date-time":"2019-07-05T03:20:36Z","timestamp":1562296836000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00373-012-1244-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,6]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2013,11]]}},"alternative-id":["1244"],"URL":"https:\/\/doi.org\/10.1007\/s00373-012-1244-1","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"value":"0911-0119","type":"print"},{"value":"1435-5914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,6]]}}}