Splitter Theorems for Cubic Graphs

Let ;k g be the class of k-connected cubic graphs of girth at least g. For several choices of k and g, we determine a set Ok g of graph operations, for which, if G and H are graphs in ;k g , G 6= H, and G contains H topologically, then some operation in Ok g can be applied to G to result in a smaller graph G0 in ;k g such that, on one hand, G0 is contained in G topologically, and on the other hand, G0 contains H topologically. Research partially supported by NSF grant DMS-9970329 and AFOSR grant F49620-01-1-0264. 

• Type: Journal
• Year: 2006
• Where: CPC
• Authors: Guoli Ding, Jinko Kanno
• Keywords: CPC 2006, Cubic Graphs, Graph Operations, Topologically