Cyclically five-connected cubic graphs

摘要

Abstract A cubic graph G is cyclically 5-connected if G is simple, 3-connected, has at least 10 vertices and for every set F of edges of size at most four, at most one component of G F contains circuits. We prove that if G and H are cyclically 5-connected cubic graphs and H topologically contains G, then either G and H are isomorphic, or (modulo well-described exceptions) there exists a cyclically 5-connected cubic graph G ′ such that H topologically contains G ′