The decycling number of a planar graph covered by K4-subgraphs
Dengju Ma, Mingyuan Ma, Han Ren · Discussiones Mathematicae Graph Theory · 2022
Let G be a planar graph of n vertices.The paper shows that the decycling number of G is at most n-1 2 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 n 2 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.