A characterization of internally 4-connected $\{P_{10}− \{v_1,v_2\}\}$-minor-free graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 731-742 Cet article a éte moissonné depuis la source Library of Science

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Let P_10 be the Petersen graph. Let V_8^– =P_10-{v_1, v_2}, where v_1 and v_2 are the adjacent vertices of P_10. In this paper, all internally 4-connected graphs that do not contain V_8^– as a minor are charaterized.
Keywords: internally $4$-connected, $V_{8}^{--}$-minor-free, Petersen graph, $2$-con\-nected minor
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Zhou, Xiaomin; Yang, Weihua; Guan, Xiaxia; Qin, Chengfu. A characterization of internally 4-connected $\{P_{10}− \{v_1,v_2\}\}$-minor-free graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 731-742. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a9/

[1] N. Ananchuen and C. Lewchalermvongs, Internally 4-connected graphs with no {cube,V8}-minor, Discuss. Math. Graph Theory 41 (2021) 481–501. https://doi.org/10.7151/dmgt.2205

[2] C. Chun, D. Mayhew and J. Oxley, Constructing internally 4-connected binary matroids, Adv. Appl. Math. 50 (2013) 16–45. https://doi.org/10.1016/j.aam.2012.03.005

[3] G. Ding, A characterization of graphs with no octahedron minor, J. Graph Theory 74 (2013) 143–162. https://doi.org/10.1002/jgt.21699

[4] G. Ding, C. Lewchalermvongs and J. Maharry, Graphs with no \overline{P}7-minor, Electron. J. Combin. 23(2) (2016) #P2.16. https://doi.org/10.37236/5403

[5] G. Ding and C. Liu, Excluding a small minor, Discrete Appl. Math. 161 (2013) 355–368. https://doi.org/10.1016/j.dam.2012.09.001

[6] M.N. Ellingham, E.A. Marshall, K. Ozeki and S. Tsuchiya, A characterization of K2,4-minor-free graphs, SIAM J. Discrete Math 30 (2014) 955–975. https://doi.org/10.1137/140986517

[7] Z. Gaslowitz, E.A. Marshall and L. Yepremyan, The characterization of planar, 4-connected, K {2, 5}-minor-free graphs (2015). arXiv: 1507.06800

[8] H. Hadwiger, Über eine Klassifikation der Streckenkomplexe, Vierteljahresschr. Naturforsch. Ges. Zürich 88 (1943) 133–143.

[9] J. Maharry, A characterization of graphs with no cube minor, J. Combin. Theory Ser. B 80 (2000) 179–201. https://doi.org/10.1006/jctb.2000.1968

[10] J. Maharry, An excluded minor theorem for the octahedron plus an edge, J. Graph Theory 57 (2008) 124–130. https://doi.org/10.1002/jgt.20272

[11] J. Maharry and N. Robertson, The structure of graphs not topologically containing the Wagner graph, J. Combin. Theory Ser. B 121 (2016) 398–420. https://doi.org/10.1016/j.jctb.2016.07.011

[12] N. Martinov, Uncontractable 4-connected graphs, J. Graph Theory 6 (1982) 343–344. https://doi.org/10.1002/jgt.3190060310

[13] W.T. Tutte, On the algebraic theory of graph colorings, J. Combin. Theory 1 (1966) 15–50. https://doi.org/10.1016/S0021-9800(66)80004-2