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5-connected graph; contractible subgraph; minor minimally $k$-connected

References:

[1] Ando, K., Qin, C.: **Some structural properties of minimally contraction-critically $5$-connected graphs**. Discrete Math. 311 (2011), 1084-1097. DOI 10.1016/j.disc.2010.10.022 | MR 2793219 | Zbl 1222.05128

[2] Bondy, J. A., Murty, U. S. R.: **Graph Theory with Applications**. American Elsevier Publishing New York (1976). MR 0411988

[3] Fijavž, G.: **Graph Minors and Connectivity. Ph.D. Thesis**. University of Ljubljana (2001).

[4] Kriesell, M.: **Triangle density and contractibility**. Comb. Probab. Comput. 14 (2005), 133-146. DOI 10.1017/S0963548304006601 | MR 2128086 | Zbl 1059.05065

[5] Kriesell, M.: **How to contract an essentially $6$-connected graph to a $5$-connected graph**. Discrete Math. 307 (2007), 494-510. DOI 10.1016/j.disc.2005.09.040 | MR 2287490 | Zbl 1109.05062

[6] Mader, W.: **Generalizations of critical connectivity of graphs**. Proceedings of the first Japan conference on graph theory and applications. Hakone, Japan, June 1-5, 1986. Discrete Mathematics {\it 72} J. Akiyama, Y. Egawa, H. Enomoto North-Holland Amsterdam (1988), 267-283. DOI 10.1016/0012-365X(88)90216-6 | MR 0975546

[7] Qin, C., Yuan, X., Su, J.: **Triangles in contraction critical $5$-connected graphs**. Australas. J. Comb. 33 (2005), 139-146. MR 2170354 | Zbl 1077.05055

[8] Tutte, W. T.: **A theory of $3$-connected graphs**. Nederl. Akad. Wet., Proc., Ser. A 64 (1961), 441-455. MR 0140094 | Zbl 0101.40903