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-connecte...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.展开更多
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。
文摘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.
