Geodesic
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

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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/