Excluded minors in cubic graphs

摘要

Let G be a cubic graph, with girth at least five, such that for every partition X, Y of its vertex set with vertical bar X vertical bar, vertical bar Y vertical bar >= 7 there are at least six edges between X and Y. We prove that if there is no homeomorphic embedding of the Petersen graph in G, and G is not one particular 20-vertex graph, then either