{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T04:55:37Z","timestamp":1725512137734},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540706656"},{"type":"electronic","value":"9783540706663"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-70666-3_2","type":"book-chapter","created":{"date-parts":[[2007,6,26]],"date-time":"2007-06-26T00:16:03Z","timestamp":1182816963000},"page":"10-20","source":"Crossref","is-referenced-by-count":1,"title":["Contractible Edges in a k-Connected Graph"],"prefix":"10.1007","author":[{"given":"Kiyoshi","family":"Ando","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"2_CR1","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.disc.2004.08.021","volume":"293","author":"K. Ando","year":"2005","unstructured":"Ando, K.: Trivially Noncontractible Edges in a Contraction Critically 5-Connected Graph. Disc. Math.\u00a0293, 61\u201372 (2005)","journal-title":"Disc. Math."},{"key":"2_CR2","unstructured":"Ando, K.: A Local Structure Theorem of 5-Connected Graphs. Preprint"},{"key":"2_CR3","unstructured":"Ando, K., Egawa, Y.: Contractible Edges in a 4-Connected Graph with Vertices of Degree Greater than 4. Preprint"},{"key":"2_CR4","unstructured":"Ando, K., Egawa, Y.: Edges not Contained in Triangles and the Distribution of Contractible Edges in a 4-Connected Graph. Preprint"},{"issue":"1","key":"2_CR5","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0095-8956(87)90065-7","volume":"42","author":"K. Ando","year":"1987","unstructured":"Ando, K., Enomoto, H., Saito, A.: Contractible Edges in 3-Connected Graphs. J. Combin. Theory Ser. B\u00a042(1), 87\u201393 (1987)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"2_CR6","doi-asserted-by":"crossref","first-page":"99","DOI":"10.55937\/sut\/991985541","volume":"36","author":"K. Ando","year":"2000","unstructured":"Ando, K., Kawarabayashi, K., Kaneko, A.: Contractible Edges in Minimally k-Connected Graphs. SUT J. Math.\u00a036(1), 99\u2013103 (2000)","journal-title":"SUT J. Math."},{"key":"2_CR7","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00373-004-0591-y","volume":"21","author":"K. Ando","year":"2005","unstructured":"Ando, K., Kaneko, A., Kawarabayashi, K.: Vertices of Degree 5 in a Contraction Critically 5-Connected Graphs. Graphs Combin.\u00a021, 27\u201337 (2005)","journal-title":"Graphs Combin."},{"key":"2_CR8","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0012-365X(03)00228-0","volume":"273","author":"K. Ando","year":"2003","unstructured":"Ando, K., Kaneko, A., Kawarabayashi, K.: Vertices of Degree 6 in a Contraction Critically 6-Connected Graph. Discrete Math.\u00a0273, 55\u201369 (2003)","journal-title":"Discrete Math."},{"key":"2_CR9","unstructured":"Ando, K., Kaneko A., Kawarabayashi, K.: Vertices of Degree 7 in a Contraction Critically 7-Connected Graph. Preprint"},{"key":"2_CR10","unstructured":"Ando, K., Kaneko, A., Kawarabayashi, K.: Some Sufficient Conditions for a k-Connected Graph to Have a k-Contractible Edge. Preprint"},{"key":"2_CR11","first-page":"239","volume":"64","author":"K. Ando","year":"2002","unstructured":"Ando, K., Kaneko, A., Kawarabayashi, K., Yoshimoto, K.: Contractible Edges and Bowties in a k-Connected Graph. Ars. Combin.\u00a064, 239\u2013247 (2002)","journal-title":"Ars Combin."},{"key":"2_CR12","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0012-365X(02)00598-8","volume":"267","author":"K. Ando","year":"2003","unstructured":"Ando, K., Kawarabayashi, K.: Some Forbidden Subgraph Conditions for a Graph to Have a k-Contractible Edge. Discrete Math.\u00a0267, 3\u201311 (2003)","journal-title":"Discrete Math."},{"key":"2_CR13","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF01789459","volume":"7","author":"Y. Egawa","year":"1991","unstructured":"Egawa, Y.: Contractible Edges in n-Connected Graphs with Minimum Degree Greater than or Equal to $[\\frac{5n}{4}]$ . Graphs Combin.\u00a07, 15\u201321 (1991)","journal-title":"Graphs Combin."},{"key":"2_CR14","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/BF02579387","volume":"6","author":"Y. Egawa","year":"1986","unstructured":"Egawa, Y., Enomoto, H., Saito, A.: Contractible Edges in Triangle-Free Graphs. Combinatorica\u00a06, 269\u2013274 (1986)","journal-title":"Combinatorica"},{"key":"2_CR15","first-page":"289","volume":"287","author":"M. Fontet","year":"1978","unstructured":"Fontet, M.: Graphes 4-Essentiels. C. R. Acad. Sci. Paris\u00a0287, 289\u2013290 (1978)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"2_CR16","first-page":"165","volume":"24","author":"K. Kawarabayashi","year":"2001","unstructured":"Kawarabayashi, K.: Note on k-Contractible Edges in k-Connected Graphs. Australas. J. Combin. Combin.\u00a024, 165\u2013168 (2001)","journal-title":"Australas. J. Combin. Combin."},{"issue":"1","key":"2_CR17","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1006\/jctb.2000.2024","volume":"82","author":"M. Kriesell","year":"2001","unstructured":"Kriesell, M.: A Degree Sum Condition for the Existence of a Contractible Edge in a k-Connected Graph. J. Combin. Theory Ser. B\u00a082(1), 81\u2013101 (2001)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"2_CR18","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1006\/jctb.2000.1960","volume":"80","author":"M. Kriesell","year":"2000","unstructured":"Kriesell, M.: Contractible Subgraphs in 3-Connected graphs. J. Combin. Theory Ser. B\u00a080(1), 32\u201348 (2000)","journal-title":"J. Combin. Theory Ser. B"},{"key":"2_CR19","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/S0195-6698(85)80048-2","volume":"6","author":"W. Mader","year":"1985","unstructured":"Mader, W.: Disjunkte Fragmente in kritisch n-Fach Zusammenh\u00e4ngende Graphen. European J. Combin.\u00a06, 353\u2013359 (1985)","journal-title":"European J. Combin."},{"key":"2_CR20","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/0012-365X(88)90216-6","volume":"72","author":"W. Mader","year":"1988","unstructured":"Mader, W.: Generalizations of Critical Connectivity of Graphs. Discrete Math.\u00a072, 267\u2013283 (1988)","journal-title":"Discrete Math."},{"key":"2_CR21","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1002\/jgt.3190060310","volume":"6","author":"N. Martinov","year":"1982","unstructured":"Martinov, N.: Uncontractible 4-Connected Graphs. J. Graph Theory\u00a06, 343\u2013344 (1982)","journal-title":"J. Graph Theory"},{"key":"2_CR22","first-page":"299","volume":"29","author":"W. McCuaig","year":"1990","unstructured":"McCuaig, W.: Edge Contractions in 3-Connected Graphs. Ars. Combin.\u00a029, 299\u2013308 (1990)","journal-title":"Ars Combin."},{"key":"2_CR23","unstructured":"Li, X., Yuan, X.: private communication"},{"key":"2_CR24","unstructured":"Li, M., Yuan, X., Su, J.: Vertex of Degree 7 in a Contraction Critical 7-Connected Graph. Preprint"},{"issue":"4","key":"2_CR25","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/BF01864172","volume":"4","author":"K. Ota","year":"1988","unstructured":"Ota, K.: The Number of Contractible Edges in 3-Connected Graphs. Graphs Combin.\u00a04(4), 333\u2013354 (1988)","journal-title":"Graphs Combin."},{"key":"2_CR26","unstructured":"Qin, C., Yuan, X., Su, J.: Some Properties of Contraction-critical 5-Connected Graphs. Preprint"},{"key":"2_CR27","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1002\/jgt.3190050403","volume":"5","author":"C. Thomassen","year":"1981","unstructured":"Thomassen, C.: Non-Separating Cycles in k-Connected Graphs. J. Graph Theory\u00a05, 351\u2013354 (1981)","journal-title":"J. Graph Theory"},{"key":"2_CR28","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S1385-7258(61)50045-5","volume":"23","author":"W.T. Tutte","year":"1961","unstructured":"Tutte, W.T.: A Theory of 3-Connected Graphs. Indag. Math.\u00a023, 441\u2013455 (1961)","journal-title":"Indag. Math."},{"issue":"4","key":"2_CR29","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1017\/S0963548302005497","volume":"12","author":"H. Wu","year":"2003","unstructured":"Wu, H.: Contractible Elements in Graphs and Matroids. Combin. Probab. Comput.\u00a012(4), 457\u2013465 (2003)","journal-title":"Combin. Probab. Comput."},{"issue":"2","key":"2_CR30","first-page":"38","volume":"25","author":"Q. Zhao","year":"2005","unstructured":"Zhao, Q., Qin, C., Yuan, X., Li, M.: Vertices of Degree 6 in a Contraction-Critical 6 Connected Graph. Journal of Guangxin Normal University\u00a025(2), 38\u201343 (2005)","journal-title":"Journal of Guangxin Normal University"}],"container-title":["Lecture Notes in Computer Science","Discrete Geometry, Combinatorics and Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-70666-3_2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T17:38:28Z","timestamp":1683913108000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-70666-3_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540706656","9783540706663"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-70666-3_2","relation":{},"subject":[]}}