%0 Journal Article
%A Xiao-min ZHOU
%A Xia-xia GUAN
%A Cheng-fu QIN
%A Wei-hua YANG
%T The Characterization of Graphs with No 2-connected Spanning Subgraph of *V*_{8} as a Minor
%D 2022
%R 10.1007/s10255-022-1022-7
%J 应用数学学报(英文)
%P 902-915
%V 38
%N 4
%X It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory. Let *V*_{8} be a graph constructed from an 8-cycle by connecting the antipodal vertices. There are thirteen 2-connected spanning subgraphs of *V*_{8}. In particular, one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs. In this paper, we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of *V*_{8} as a forbidden minor.
%U https://applmath.cjoe.ac.cn/jweb_yysxxb_en/CN/10.1007/s10255-022-1022-7