A 3-connected graph is called 3 +-connected if it has no 3-separation that separates a "large" fan or K 3,n from the rest of the graph. It is proved in this paper that except for K 4, every 3 +-connected graph has a 3 +-connected proper minor that is at most two edges away from the original graph. This result is used to characterize Q-minor-free graphs, where Q is obtained from the cube by contracting an edge. © 2012 Society for Industrial and Applied Mathematics.
Publication Source (Journal or Book title)
SIAM Journal on Discrete Mathematics
Ding, G., & Liu, C. (2012). A chain theorem for 3 +-connected graphs. SIAM Journal on Discrete Mathematics, 26 (1), 102-113. https://doi.org/10.1137/110834408