The Characterization of Graphs with No 2-connected Spanning Subgraph of V_(8)as a Minor  

作　　者：Xiao-min ZHOU Xia-xia GUAN Cheng-fu QIN Wei-hua YANG 

机构地区：[1]Department of Mathematics,Taiyuan University of Technology,Taiyuan 030000,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China [3]School of Mathematics Science,Guangxi Teachers Education University,Nanning 530001,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第4期902-915,共14页应用数学学报（英文版）

基　　金：Research Project supported by the National Natural Science Foundation of China(No.11961051);Provincial Natural Science Foundation of Shanxi(20210302123097);Shanxi Scholarship Council of China。

摘　　要：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.

关 键 词：V_(8) internally 4-connected graph minor-free 2-connected subgraph 

分 类 号：O157.5[理学—数学]