Geodesic
The decycling number of a planar graph covered by $K_4$-subgraphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 459-473

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Let G be a planar graph of n vertices. The paper shows that the decycling number of G is at most n-12 if G has not any K_4-minor. If the maximum degree of G is at most four and G is not 4-regular, the paper proves that the decycling number of G is n2 if and only if G is covered by K_4-subgraphs. In addition, the decycling number of G covered by octahedron-subgraphs or icosahedron-subgraphs is studied.
Keywords: decycling number, planar graph, $K_4$-minor 
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Ma, Dengju; Ma, Mingyuan; Ren, Han. The decycling number of a planar graph covered by $K_4$-subgraphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 459-473. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a2/